The sphericalp-spin interaction spin glass model: the statics
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Unlike the dCGHS case, the analytic continuation of the replica-symmetric ansatz (5.9) in (5.7) to imaginary m obeys the boundedness condition |Z_iα|≤1; however Z_m still exhibits superexponential growth for real m, so Carlson's theorem is still inapplicable.
“Though we note that unlike the d CGHS case discussed in Sec.III B, the analytic continuation of the replica-symmetric ansatz (5.9) in (5.7) to imaginary m does indeed obey the boundedness condition jZ iα j ≤ 1.However, Z m still exhibits superexponential growth for real m, so Carlson's theorem is still inapplicable [66].”
From Free energy from replica wormholes (2021) · cites this paper as [66]
For positive integer m, the dominant saddles exhibit replica symmetry.
“Indeed, for positive integer m, the dominant saddles do exhibit this symmetry [66].”
From Free energy from replica wormholes (2021) · cites this paper as [66]
Cites
Theory of dynamic critical phenomena
Hohenberg, P. C., & Halperin, B. I. (1977) · Reviews of Modern Physics · doi:10.1103/revmodphys.49.435 · Cited by 6,933 · see citing works
Solvable Model of a Spin-Glass
Sherrington, D., & Kirkpatrick, S. (1975) · Physical Review Letters · doi:10.1103/physrevlett.35.1792 · Cited by 3,577 · see citing works
Mézard, M., Giorgio Parisi, A., VIRASORO, M. A., & Thouless, D. J. (1988) · Physics Today · doi:10.1063/1.2811676 · Cited by 2,683 · see citing works
Stability of the Sherrington-Kirkpatrick solution of a spin glass model
Almeida, J. R. L. D., & Thouless, D. J. (1978) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/11/5/028 · Cited by 2,061 · see citing works
Infinite Number of Order Parameters for Spin-Glasses
Parisi, G. (1979) · Physical Review Letters · doi:10.1103/physrevlett.43.1754 · Cited by 1,140 · see citing works
Infinite-ranged models of spin-glasses
Kirkpatrick, S., & Sherrington, D. (1978) · Physical review. B, Condensed matter · doi:10.1103/physrevb.17.4384 · Cited by 1,015 · see citing works
Dynamical model of the liquid-glass transition
Leutheusser, E. (1984) · Physical Review A · doi:10.1103/physreva.29.2765 · Cited by 1,010 · see citing works
Order Parameter for Spin-Glasses
Parisi, G. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.1946 · Cited by 862 · see citing works
p -spin-interaction spin-glass models: Connections with the structural glass problem
Kirkpatrick, T. R., & Thirumalai, D. (1987) · Physical review. B, Condensed matter · doi:10.1103/physrevb.36.5388 · Cited by 545 · see citing works
Nature of the Spin-Glass Phase
Mézard, M., Giorgio Parisi, A., Sourlas, N., Toulouse, G., & VIRASORO, M. A. (1984) · Physical Review Letters · doi:10.1103/physrevlett.52.1156 · Cited by 534 · see citing works
Gross, D. J., & Mézard, M. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90237-2 · Cited by 497 · see citing works
Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses
Sompolinsky, H., & Zippelius, A. (1982) · Physical review. B, Condensed matter · doi:10.1103/physrevb.25.6860 · Cited by 486 · see citing works
Spin glasses with p-spin interactions
Gardner, E. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90374-8 · Cited by 424 · see citing works
Dynamics of the Structural Glass Transition and the p -Spin—Interaction Spin-Glass Model
Kirkpatrick, T. R., & Thirumalai, D. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.2091 · Cited by 393 · see citing works
Time-Dependent Order Parameters in Spin-Glasses
Sompolinsky, H. (1981) · Physical Review Letters · doi:10.1103/physrevlett.47.935 · Cited by 380 · see citing works
Spherical Model of a Spin-Glass
Kosterlitz, J. M., Thouless, D. J., & Jones, R. C. (1976) · Physical Review Letters · doi:10.1103/physrevlett.36.1217 · Cited by 375 · see citing works
Crisanti, A., Paladin, G., & Vulpiani, A. (1993) · Springer series in solid-state sciences · doi:10.1007/978-3-642-84942-8 · Cited by 303 · see citing works
Self-citationSome aspects of phase transitions described by the self consistent current relaxation theory
G�tze, W. (1984) · The European Physical Journal B · doi:10.1007/bf01469695 · Cited by 178 · see citing works
Eigenvalues of the stability matrix for Parisi solution of the long-range spin-glass
Dominicis, C. D., & Kondor, I. (1983) · Physical review. B, Condensed matter · doi:10.1103/physrevb.27.606 · Cited by 133 · see citing works
Dynamics of learning for the binary perceptron problem
Horner, H. (1992) · The European Physical Journal B · doi:10.1007/bf01313839 · Cited by 85 · see citing works
Dynamics of manifolds in random media: the selfconsistent Hartree approximation
Kinzelbach, H., & Horner, H. (1993) · Journal de Physique I · doi:10.1051/jp1:1993183 · Cited by 42 · see citing works
Dynamics of learning and generalization in a binary perceptron model
Horner, H. (1992) · The European Physical Journal B · doi:10.1007/bf01309290 · Cited by 33 · see citing works
Dynamics of the finite SK spin-glass
Kinzelbach, H., & Horner, H. (1991) · The European Physical Journal B · doi:10.1007/bf01453763 · Cited by 18 · see citing works
Properties of an adiabatically cooled SK spin glass
Freixa-Pascual, M., & Horner, H. (1990) · The European Physical Journal B · doi:10.1007/bf01390654 · Cited by 17 · see citing works
Dynamic scaling for spin glasses near the de Almeida-Thouless line
Sommers, H.-J., & Fischer, K. H. (1985) · The European Physical Journal B · doi:10.1007/bf01304264 · Cited by 16 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model
Cugliandolo, L. F., & Jorge Kurchan, B. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.173 · Cited by 994 · see citing works
Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics
Cugliandolo, L. F., Jorge Kurchan, B., & Peliti, L. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.55.3898 · Cited by 803 · see citing works
Spin-glass theory for pedestrians
Castellani, T., & Cavagna, A. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/05/p05012 · Cited by 472 · see citing works
Mode-coupling theory and the glass transition in supercooled liquids
Das, S. P. (2004) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.785 · Cited by 392 · see citing works
Crisanti, A., & Ritort, F. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/21/201 · Cited by 375 · see citing works
Self-citationThe sphericalp-spin interaction spin-glass model
Crisanti, A., Horner, H., & Sommers, H.-J. (1993) · The European Physical Journal B · doi:10.1007/bf01312184 · Cited by 303 · see citing works
Self-citationRecent advances and applications of random lasers and random fiber lasers
Gomes, A. S. L., Moura, A. L., de Araujo, C. B., & Raposo, E. P. (2021) · Progress in Quantum Electronics · doi:10.1016/j.pquantelec.2021.100343 · Cited by 243 · see citing works
Statistical Mechanics of Deep Learning
Bahri, Y., Kadmon, J., Pennington, J., Schoenholz, S. S., Sohl‐Dickstein, J., & Ganguli, S. (2019) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031119-050745 · Cited by 237 · see citing works
Phase Diagram of Coupled Glassy Systems: A Mean-Field Study
Franz, S., & Giorgio Parisi, A. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2486 · Cited by 219 · see citing works
Phase space geometry and slow dynamics
Jorge Kurchan, B., & Laloux, L. (1996) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/29/9/009 · Cited by 191 · see citing works
Full dynamical solution for a spherical spin-glass model
Cugliandolo, L. F., & Dean, D. S. (1995) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/28/15/003 · Cited by 183 · see citing works
Nonlinear susceptibility in glassy systems: A probe for cooperative dynamical length scales
Bouchaud, J., & Biroli, G. (2005) · Physical Review B · doi:10.1103/physrevb.72.064204 · Cited by 173 · see citing works
Stationary points of the Thouless-Anderson-Palmer free energy
Cavagna, A., Giardina, I., & Giorgio Parisi, A. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.57.11251 · Cited by 170 · see citing works
Weak ergodicity breaking in mean-field spin-glass models
Cugliandolo, L. F., & Jorge Kurchan, B. (1995) · Philosophical Magazine B · doi:10.1080/01418639508238541 · Cited by 148 · see citing works
Free energy of the spherical mean field model
Talagrand, M. (2005) · Probability Theory and Related Fields · doi:10.1007/s00440-005-0433-8 · Cited by 132 · see citing works
Topological quantum glassiness
Castelnovo, C., & Chamon, C. (2011) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2011.609152 · Cited by 130 · see citing works
Slow dynamics and aging in spin glasses
Vincent, E., Hammann, J., Ocio, M., Bouchaud, J., & Cugliandolo, L. F. (2008) · Springer eBooks · doi:10.1007/bfb0104827 · Cited by 122 · see citing works
Shear bands as manifestation of a criticality in yielding amorphous solids
Giorgio Parisi, A., Procaccia, I., Rainone, C., & Singh, M. P. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1700075114 · Cited by 116 · see citing works
Gomes, A. S. L., Raposo, E. P., Moura, A. L., Fewo, S. I., Pincheira, P. I. R., Jerez, V. A., Maia, L. J. Q., & de Araujo, C. B. (2016) · Scientific Reports · doi:10.1038/srep27987 · Cited by 119 · see citing works
Quasi-equilibrium interpretation of ageing dynamics
Franz, S., & VIRASORO, M. A. (2000) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/33/5/306 · Cited by 108 · see citing works
On the Dynamics of the Glass Transition on Bethe Lattices
Andrea Montanari, A., & Semerjian, G. (2006) · Journal of Statistical Physics · doi:10.1007/s10955-006-9103-1 · Cited by 102 · see citing works
Glassy Transition and Aging in a Model Without Disorder
Franz, S., & Hertz, J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.2114 · Cited by 105 · see citing works
Dynamics within metastable states in a mean-field spin glass
Barrat, A., Burioni, R., & Mézard, M. (1996) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/29/5/001 · Cited by 99 · see citing works
Ros, V., Arous, G. B., Biroli, G., & Cammarota, C. (2019) · Physical Review X · doi:10.1103/physrevx.9.011003 · Cited by 100 · see citing works
The complexity of spherical $p$-spin models—A second moment approach
Subag, E. (2017) · The Annals of Probability · doi:10.1214/16-aop1139 · Cited by 100 · see citing works
Cardenas, M., Franz, S., & Giorgio Parisi, A. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478028 · Cited by 99 · see citing works
Glassy behaviour in disordered systems with nonrelaxational dynamics
Cugliandolo, L. F., Jorge Kurchan, B., Doussal, P. L., & Peliti, L. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.350 · Cited by 96 · see citing works
Effective potential in glassy systems: theory and simulations
Franz, S., & Giorgio Parisi, A. (1998) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(98)00315-x · Cited by 108 · see citing works
Properties of Equilibria and Glassy Phases of the Random Lotka-Volterra Model with Demographic Noise
Altieri, A., Roy, F., Cammarota, C., & Biroli, G. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.258301 · Cited by 96 · see citing works
Cooling-schedule dependence of the dynamics of mean-field glasses
Andrea Montanari, A., & Ricci‐Tersenghi, F. (2004) · Physical Review B · doi:10.1103/physrevb.70.134406 · Cited by 94 · see citing works
Spherical 2+p spin-glass model: An analytically solvable model with a glass-to-glass transition
Crisanti, A., & Leuzzi, L. (2006) · Physical Review B · doi:10.1103/physrevb.73.014412 · Cited by 91 · see citing works
Self-citationReal-time nonequilibrium dynamics of quantum glassy systems
Cugliandolo, L. F., & Lozano, G. S. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.59.915 · Cited by 92 · see citing works
Glassiness and constrained dynamics of a short-range nondisordered spin model
Garrahan, J. P., & Newman, M. E. J. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.7670 · Cited by 91 · see citing works
Large time nonequilibrium dynamics of a particle in a random potential
Cugliandolo, L. F., & Doussal, P. L. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.53.1525 · Cited by 90 · see citing works
Free energy from replica wormholes
Engelhardt, N., Fischetti, S., & Maloney, A. (2021) · Physical Review D · doi:10.1103/physrevd.103.046021 · Cited by 90 · see citing works
Statistical and computational phase transitions in spiked tensor estimation
Lesieur, T., Miolane, L., Lelarge, M., Krząkała, F., & Zdeborová, L. (2017) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2017.8006580 · Cited by 94 · see citing works
Mean-field theory, mode-coupling theory, and the onset temperature in supercooled liquids
Brumer, Y., & Reichman, D. R. (2004) · Physical Review E · doi:10.1103/physreve.69.041202 · Cited by 87 · see citing works
Imaginary-time replica formalism study of a quantum sphericalp-spin-glass model
Cugliandolo, L. F., Grempel, D. R., & Santos, C. A. D. S. (2001) · Physical review. B, Condensed matter · doi:10.1103/physrevb.64.014403 · Cited by 86 · see citing works
Replica theory of the rigidity of structural glasses
Yoshino, H. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4722343 · Cited by 82 · see citing works
How to compute the thermodynamics of a glass using a cloned liquid
Mézard, M. (1999) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(98)00659-1 · Cited by 92 · see citing works
General Phase Diagram of Multimodal Ordered and Disordered Lasers in Closed and Open Cavities
Antenucci, F., Conti, C., Crisanti, A., & Leuzzi, L. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.043901 · Cited by 81 · see citing works
Self-citationGlassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser
Gomes, A. S. L., Lima, B. C., Pincheira, P. I. R., Moura, A. L., Gagné, M., Raposo, E. P., de Araujo, C. B., & Kashyap, R. (2016) · Physical Review A · doi:10.1103/physreva.94.011801 · Cited by 80 · see citing works
Complexity of waves in nonlinear disordered media
Conti, C., & Leuzzi, L. (2011) · Physical Review B · doi:10.1103/physrevb.83.134204 · Cited by 79 · see citing works
Spin Glass Theory and Far Beyond
Charbonneau, P., Marinari, E., Mézard, M., Giorgio Parisi, A., Ricci‐Tersenghi, F., Sicuro, G., & Zamponi, F. (2023) · WORLD SCIENTIFIC eBooks · doi:10.1142/13341 · Cited by 81 · see citing works
Spherical 2+p Spin-Glass Model: An Exactly Solvable Model for Glass to Spin-Glass Transition
Crisanti, A., & Leuzzi, L. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.217203 · Cited by 74 · see citing works
Self-citationPhase Diagram and Complexity of Mode-Locked Lasers: From Order to Disorder
Leuzzi, L., Conti, C., Folli, V., Angelani, L., & Ruocco, G. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.083901 · Cited by 74 · see citing works
Optimization of mean-field spin glasses
Alaoui, A. E., Andrea Montanari, A., & Sellke, M. (2021) · The Annals of Probability · doi:10.1214/21-aop1519 · Cited by 73 · see citing works
Folena, G., Franz, S., & Ricci‐Tersenghi, F. (2020) · Physical Review X · doi:10.1103/physrevx.10.031045 · Cited by 81 · see citing works
Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model
Baik, J., & Lee, J. O. (2016) · Journal of Statistical Physics · doi:10.1007/s10955-016-1610-0 · Cited by 68 · see citing works
Role of Unstable Directions in the Equilibrium and Aging Dynamics of Supercooled Liquids
Donati, C., Sciortino, F., & Tartaglia, P. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.1464 · Cited by 67 · see citing works
Statistical limits of spiked tensor models
Perry, A., Wein, A. S., & Bandeira, A. S. (2020) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/19-aihp960 · Cited by 66 · see citing works
Activated events in glasses: The structure of entropic droplets
Dzero, M., Schmalian, J., & Wolynes, P. G. (2005) · Physical Review B · doi:10.1103/physrevb.72.100201 · Cited by 65 · see citing works
The geometry of the Gibbs measure of pure spherical spin glasses
Subag, E. (2017) · Inventiones mathematicae · doi:10.1007/s00222-017-0726-4 · Cited by 65 · see citing works
Critical Slowing Down Exponents of Mode Coupling Theory
Caltagirone, F., Ferrari, U., Leuzzi, L., Giorgio Parisi, A., Ricci‐Tersenghi, F., & Rizzo, T. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.085702 · Cited by 66 · see citing works
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
Arous, G. B., Dembo, A., & Guionnet, A. (2006) · Probability Theory and Related Fields · doi:10.1007/s00440-005-0491-y · Cited by 65 · see citing works
Gaussian density fluctuations and mode coupling theory for supercooled liquids
Zaccarelli, E., Foffi, G., Sciortino, F., Tartaglia, P., & Dawson, K. A. (2001) · Europhysics Letters (EPL) · doi:10.1209/epl/i2001-00395-x · Cited by 62 · see citing works
Critical dynamics in glassy systems
Giorgio Parisi, A., & Rizzo, T. (2013) · Physical Review E · doi:10.1103/physreve.87.012101 · Cited by 61 · see citing works
The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models
Chen, W. (2013) · Electronic Journal of Probability · doi:10.1214/ejp.v18-2580 · Cited by 61 · see citing works
Glassy systems under time-dependent driving forces: Application to slow granular rheology
Berthier, L., Cugliandolo, L. F., & Iguain, J. L. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.63.051302 · Cited by 61 · see citing works
Exactly Solvable Model of a Quantum Spin Glass
Nieuwenhuizen, T. M. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4289 · Cited by 62 · see citing works
Quantum Thouless-Anderson-Palmer equations for glassy systems
Biroli, G., & Cugliandolo, L. F. (2001) · Physical review. B, Condensed matter · doi:10.1103/physrevb.64.014206 · Cited by 59 · see citing works
Are disordered spin glass models relevant for the structural glass problem?
Kirkpatrick, T. R., & Thirumalai, D. (1995) · Transport Theory and Statistical Physics · doi:10.1080/00411459508203940 · Cited by 59 · see citing works
Amorphous-amorphous transition and the two-step replica symmetry breaking phase
Crisanti, A., & Leuzzi, L. (2007) · Physical Review B · doi:10.1103/physrevb.76.184417 · Cited by 60 · see citing works
Self-citationFyodorov, Y. V., & Sommers, H.-J. (2006) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2006.11.029 · Cited by 54 · see citing works
Self-citationTopology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization
Fyodorov, Y. V., & Doussal, P. L. (2013) · Journal of Statistical Physics · doi:10.1007/s10955-013-0838-1 · Cited by 57 · see citing works
Role of saddles in mean-field dynamics above the glass transition
Cavagna, A., Giardina, I., & Giorgio Parisi, A. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/26/302 · Cited by 57 · see citing works
Index distribution of random matrices with an application to disordered systems
Cavagna, A., Garrahan, J. P., & Giardina, I. (2000) · Physical review. B, Condensed matter · doi:10.1103/physrevb.61.3960 · Cited by 57 · see citing works
Replica-symmetry-breaking transitions and off-equilibrium dynamics
Rizzo, T. (2013) · Physical Review E · doi:10.1103/physreve.88.032135 · Cited by 56 · see citing works
Random pinning glass transition: Hallmarks, mean-field theory and renormalization group analysis
Cammarota, C., & Biroli, G. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4790400 · Cited by 56 · see citing works
Jorge Kurchan, B. (2000) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/12/29/332 · Cited by 56 · see citing works
Effective potential in glassy systems: theory and simulations
Franz, S., & Giorgio Parisi, A. (1998) · RePEc: Research Papers in Economics · Cited by 55 · see citing works
On properties of Parisi measures
Auffinger, A., & Chen, W. (2014) · Probability Theory and Related Fields · doi:10.1007/s00440-014-0563-y · Cited by 53 · see citing works
Course 8 Dynamics of trap models
Arous, G. B., & Černý, J. (2006) · Les Houches/Les Houches · doi:10.1016/s0924-8099(06)80045-4 · Cited by 52 · see citing works
The number of solutions of the Thouless-Anderson-Palmer equations forp-spin-interaction spin glasses
Rieger, H. (1992) · Physical review. B, Condensed matter · doi:10.1103/physrevb.46.14655 · Cited by 52 · see citing works
First steps of a nucleation theory in disordered systems
Franz, S. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/04/p04001 · Cited by 52 · see citing works
Second-order dynamic transition in a p=2 spin-glass model
van Duijvendijk, K., Jack, R. L., & van Wijland, F. (2010) · Physical Review E · doi:10.1103/physreve.81.011110 · Cited by 52 · see citing works
Fyodorov, Y. V., & Bouchaud, J. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/32/324009 · Cited by 48 · see citing works
Quantum phase transition in spin glasses with multi-spin interactions
Nieuwenhuizen, T. M., & Ritort, F. (1998) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(97)00546-3 · Cited by 49 · see citing works
On the overlap in the multiple spherical SK models
Panchenko, D., & Talagrand, M. (2007) · The Annals of Probability · doi:10.1214/009117907000000015 · Cited by 51 · see citing works
Dynamics of trap modelsPreprint
Arous, G. B., & Černý, J. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0603344 · Cited by 51 · see citing works
An investigation of the hidden structure of states in a mean-field spin-glass model
Cavagna, A., Giardina, I., & Giorgio Parisi, A. (1997) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/30/20/009 · Cited by 47 · see citing works
Dissipative effects on quantum glassy systems
Cugliandolo, L. F., Grempel, D. R., Lozano, G. S., Lozza, H., & Santos, C. A. D. S. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.66.014444 · Cited by 48 · see citing works
Replica symmetry breaking in attractor neural network models
Steffan, H., & K�hn, R. (1994) · The European Physical Journal B · doi:10.1007/bf01312198 · Cited by 48 · see citing works
Topology Trivialization and Large Deviations for the Minimum in the Simplest Random OptimizationPreprint
Fyodorov, Y. V., & Doussal, P. L. (2016) · Cited by 48 · see citing works
Intermolecular Forces and the Glass Transition
Hall, R. W., & Wolynes, P. G. (2007) · The Journal of Physical Chemistry B · doi:10.1021/jp075017j · Cited by 47 · see citing works
The dynamics of the spherical p -spin model: From microscopic to asymptotic
Kim, B., & Latz, A. (2001) · Europhysics Letters (EPL) · doi:10.1209/epl/i2001-00202-4 · Cited by 46 · see citing works
Multifractality and freezing phenomena in random energy landscapes: An introduction
Fyodorov, Y. V. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.01.020 · Cited by 43 · see citing works
The extremal process of critical points of the pure p-spin spherical spin glass model
Subag, E., & Zeitouni, O. (2016) · Probability Theory and Related Fields · doi:10.1007/s00440-016-0724-2 · Cited by 46 · see citing works
Complexity of energy barriers in mean-field glassy systems
Ros, V., Biroli, G., & Cammarota, C. (2019) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/126/20003 · Cited by 46 · see citing works
How to compute the thermodynamics of a glass using a cloned liquid
Mézard, M. (1998) · Cited by 46 · see citing works
Quenched complexity of the mean-fieldp-spin spherical model with external magnetic field
Cavagna, A., Garrahan, J. P., & Giardina, I. (1999) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/32/5/004 · Cited by 46 · see citing works
On the formal equivalence of the TAP and thermodynamic methods in the SK model
Cavagna, A., Giardina, I., Giorgio Parisi, A., & zard, M. M. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/5/301 · Cited by 46 · see citing works
Ageing classification in glassy dynamics
Barrat, A., Burioni, R., & Mézard, M. (1996) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/29/7/005 · Cited by 46 · see citing works
Following the Ground States of Full‐RSB Spherical Spin Glasses
Subag, E. (2020) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.21922 · Cited by 45 · see citing works
Lévy Statistics and the Glassy Behavior of Light in Random Fiber Lasers
de Araujo, C. B., Gomes, A. S. L., & Raposo, E. P. (2017) · Applied Sciences · doi:10.3390/app7070644 · Cited by 44 · see citing works
From Second to First Order Transitions in a Disordered Quantum Magnet
Cugliandolo, L. F., Grempel, D. R., & Santos, C. A. D. S. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2589 · Cited by 43 · see citing works
Free Energy and Complexity of Spherical Bipartite Models
Auffinger, A., & Chen, W. (2014) · Journal of Statistical Physics · doi:10.1007/s10955-014-1073-0 · Cited by 43 · see citing works
Baik, J., & Lee, J. O. (2017) · Annales Henri Poincaré · doi:10.1007/s00023-017-0562-5 · Cited by 43 · see citing works
Free energy of bipartite spherical Sherrington–Kirkpatrick model
Baik, J., & Lee, J. O. (2020) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/20-aihp1062 · Cited by 42 · see citing works
Dynamical TAP approach to mean field glassy systems
Biroli, G. (1999) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/32/48/301 · Cited by 40 · see citing works
- Authors
- Crisanti, A., & Sommers, H. J.
- Affiliations
- University of L'Aquila (IT)
- University of Duisburg-Essen (DE)
- ORCID
- Crisanti, A.
- Venue
- Zeitschrift f�r Physik B Condensed Matter
- Published
- 1992-10
- Volume
- 87
- Issue
- 3
- Pages
- 341-354
- ISSN
- 1434-6028 (ISSN-L)
- 0722-3277
- 1434-6036
- OpenAlex
- W2048964254
- Cited by
- 481
- References
- 25
- Citations by year
- 2026: 7 · 2025: 25 · 2024: 22 · 2023: 27 · 2022: 32 · 2021: 29 · 2020: 29 · 2019: 21 · 2018: 15 · 2017: 16 · 2016: 11 · 2015: 11 · 2014: 11 · 2013: 18 · 2012: 11
- FWCI
- 3.93
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- The European Physical Journal B (publishedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Materials Science › Materials Chemistry › Material Dynamics and Properties
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- spherical p-spin model, spin glass, replica symmetry breaking, metastable states, external magnetic field, static characteristics, spin-glass transition
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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