The Theory of Critical Phenomena: An Introduction to the Renormalization Group

Perturbative calculation of critical exponents for the Bose–Hubbard model

Hinrichs, D., Pelster, A., & Holthaus, M. (2013) · Applied Physics B · doi:10.1007/s00340-013-5419-0 · Cited by 13

Effect of ferromagnetic proximity on critical behavior

Ahlberg, M., Korelis, P., Andersson, G., et al. (2012) · Physical Review B · doi:10.1103/physrevb.85.224425 · Cited by 13

Effective two-dimensional description from critical phenomena in black holes

Loustó, C. O. (1995) · General Relativity and Gravitation · doi:10.1007/bf02107952 · Cited by 13

Multiscale analysis of information correlations in an infinite-range, ferromagnetic Ising system

Gheorghiu-Svirschevski, S., & Bar‐Yam, Y. (2004) · Physical Review E · doi:10.1103/physreve.70.066115 · Cited by 13

Observable Properties of Quark--Hadron Phase Transition at the Large Hadron Collider

Hwa, R. C., & Yang, C. B. (2017) · Acta Physica Polonica B · doi:10.5506/aphyspolb.48.23 · Cited by 13

Renormalization group crossover in the critical dynamics of field theories with mode coupling terms

Cavagna, A., Carlo, L. D., Giardina, I., Grandinetti, L., Grigera, T. S., & Pisegna, G. (2019) · Physical review. E · doi:10.1103/physreve.100.062130 · Cited by 15

Discovering Noncritical Organization: Statistical Mechanical, Information Theoretic, and Computational Views of Patterns in One-Dimensional Spin Systems

Feldman, D. P., & Crutchfield, J. P. (2022) · Entropy · doi:10.3390/e24091282 · Cited by 13

Polymorphic phase transitions in systems evolving in a two-dimensional discrete space

Gadomski, A. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.60.1252 · Cited by 13

Blends of Polybutadiene with Different Vinyl Contents and Polystyrene Studied with Small-Angle Neutron Scattering in Varying Temperature and Pressure Fields

Frielinghaus, H., Schwahn, D., & Willner, L. (2001) · Macromolecules · doi:10.1021/ma001015k · Cited by 13

Biodiversity power laws

Marquet, P. A., Abades, S. R., & Labra, F. A. (2007) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814938.023 · Cited by 14

Learning dynamics of simple perceptrons with non-extensive cost functions

Cannas, S. A., Stariolo, D. A., & Tamarit, F. A. (1996) · Network Computation in Neural Systems · doi:10.1080/0954898x.1996.11978659 · Cited by 13

Spontaneous symmetry breaking in a NO + CO surface reaction model

Kortlüke, O., Kuzovkov, V. N., & von Niessen, W. (1997) · Chemical Physics Letters · doi:10.1016/s0009-2614(97)00721-5 · Cited by 13

Specific heat and isothermal magnetocaloric effect in UNi0.5Sb2

Plackowski, T., Kaczorowski, D., & Bukowski, Z. (2005) · Physical Review B · doi:10.1103/physrevb.72.184418 · Cited by 13

STRUCTURED PSYCHOSOCIAL STRESS AND THE US OBESITY EPIDEMIC

Wallace, R., & Wallace, D. (2005) · Journal of Biological Systems · doi:10.1142/s0218339005001574 · Cited by 15

The fcc - bcc structural transition: II. A mean field model for finite-temperature effects.

Mohn, P., Schwarz, K., & Blaha, P. (1996) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/8/7/007 · Cited by 13

Diffusion in 2D Quasi-Crystals

Joseph, D., Michael Baake, A., Krämer, P., & Trebin, H. (1994) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/27/6/007 · Cited by 13

Experimental observation of multicritical points with TGB phases on a pure compound

Anakkar, A., Daoudi, A., Buisine, J. M., et al. (1996) · Liquid Crystals · doi:10.1080/02678299608032054 · Cited by 13

Dynamic hysteresis at a noisy saddle node shows power-law scaling but nonuniversal exponent.

Kundu, S., Patel, R. K., Middey, S., & Bansal, B. (2023) · Physical Review E · doi:10.1103/physreve.108.024101 · Cited by 11

Local order metrics for many-particle systems across length scales

Maher, C. E., & Torquato, S. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033262 · Cited by 12

Network renormalization

Gabrielli, A., Garlaschelli, D., Patil, S. P., & Serrano, M. Á. (2025) · Nature Reviews Physics · doi:10.1038/s42254-025-00817-5 · Cited by 22

Microscopic approach to orientational order of domain walls

Barci, D. G., & Stariolo, D. A. (2011) · Physical Review B · doi:10.1103/physrevb.84.094439 · Cited by 12

Six-Vertex Model

Eckle, H.-P. (2019) · Oxford University Press eBooks · doi:10.1093/oso/9780199678839.003.0011 · Cited by 16

$$ \mathcal{PT} $$ breaking and RG flows between multicritical Yang-Lee fixed points

Lencsés, M., Miscioscia, A., Mussardo, G., et al. (2023) · Journal of High Energy Physics · doi:10.1007/jhep09(2023)052 · Cited by 12

Theorems as Constructive Visions

Longo, G. (2012) · New ICMI studies series · doi:10.1007/978-94-007-2129-6_3 · Cited by 12

Membrane Elasticity and Mediated Interactions in Continuum Theory: A Differential Geometric Approach

Deserno, M. (2009) · Humana Press eBooks · doi:10.1007/978-1-60761-314-5_2 · Cited by 12

Adaptive chronic infection, structured stress, and medical magic bullets: do reductionist cures select for holistic diseases?

Wallace, R., & Wallace, R. G. (2004) · Biosystems · doi:10.1016/j.biosystems.2004.04.004 · Cited by 16

Equilibrium properties of the condensed states of a turbulent two-dimensional neutral vortex system

Viecelli, J. A. (1995) · Physics of Fluids · doi:10.1063/1.868528 · Cited by 12

Coarse-grained models of stripe forming systems: Phase diagrams, anomalies, and scaling hypothesis

Mendoza-Coto, A., & Stariolo, D. A. (2012) · Physical Review E · doi:10.1103/physreve.86.051130 · Cited by 12

Evaluating Characteristic Parameters for Carbon Dioxide in the Sanchez–Lacombe Equation of State

von Konigslow, K., Park, C. B., & Thompson, R. B. (2017) · Journal of Chemical & Engineering Data · doi:10.1021/acs.jced.6b00743 · Cited by 12

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature

Zhong, W., Panja, D., Barkema, G. T., et al. (2018) · Physical review. E · doi:10.1103/physreve.98.012124 · Cited by 12

Correlation Lengths in the Language of Computable Information

Martiniani, S., Lemberg, Y., Chaikin, P. M., & Levine, D. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.170601 · Cited by 13

Generalized boundary conditions for periodic lattice systems: Application to the two-dimensional Ising model on a square lattice

Etxebarria, I., Elcoro, L., & Perez-Mato, J. M. (2004) · Physical Review E · doi:10.1103/physreve.70.066133 · Cited by 12

Generalized Kelvin equation and pseudospinodal in nucleation theory

Kalikmanov, V. I. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2958919 · Cited by 12

Critical Casimir forces for O(N) models from functional renormalization

Jakubczyk, P., & Napiórkowski, M. (2013) · Physical Review B · doi:10.1103/physrevb.87.165439 · Cited by 12

Chaos vs linear instability in the Vlasov equation: A fractal analysis characterization

Atalmi, A., Baldo, M., Burgio, G. F., & Rapisarda, A. (1996) · Physical Review C · doi:10.1103/physrevc.53.2556 · Cited by 12

Cluster translation and growth in density functional theories of homogeneous nucleation

Barrett, J. C. (1997) · The Journal of Chemical Physics · doi:10.1063/1.475061 · Cited by 12

Classical-nonclassical crossover behavior of critical and noncritical liquid binary solutions in a strong electric field

Zioło, J., & Rzoska, S. J. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.60.4983 · Cited by 12

Lie algebra of anomalously scaled fluctuations

Broidioi, M., Momont, B., & Verbeure, A. F. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531343 · Cited by 12

Dynamically Driven Renormalization GroupPreprint

Vespignani, A., & Loreto, V. (2008) · Cited by 12

Scaling Phenomena and the Emergence of Complexity in Astrobiology

Pérez‐Mercader, J. (2002) · Astrobiology · doi:10.1007/978-3-642-59381-9_22 · Cited by 11

Free power dissipation from functional line integration

Brader, J. M., & Schmidt, M. (2015) · Molecular Physics · doi:10.1080/00268976.2015.1042086 · Cited by 11

Error analysis of a compact finite difference method for fourth-order nonlinear elliptic boundary value problems

Wang, Y.-M. (2017) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2017.04.011 · Cited by 11

Heisenberg scaling with classical long-range correlations

Fernández-Lorenzo, S., Dunningham, J., & Porras, D. (2018) · Physical Review A · doi:10.1103/physreva.97.023843 · Cited by 11

Magnetic ground state of the one-dimensional ferromagnetic chain compounds M(NCS)2(thiourea)2 ( M=Ni,Co )

Curley, S. P. M., Scatena, R., Williams, R. C., et al. (2021) · Physical Review Materials · doi:10.1103/physrevmaterials.5.034401 · Cited by 11

Varied phenomenology of models displaying dynamical large-deviation singularities

Whitelam, S., & Jacobson, D. (2021) · Physical review. E · doi:10.1103/physreve.103.032152 · Cited by 11

Real-space renormalization-group study of the phase transition in a Gaussian model of fractals

Li, S., & Yang, Z. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.55.6656 · Cited by 11

Short-time dynamics of a metamagnetic model

Santos, M., & Figueiredo, W. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.1799 · Cited by 11

Correlated effective field theory in transition metal compounds

Mukhopadhyay, S., & Chatterjee, I. (2003) · Journal of Magnetism and Magnetic Materials · doi:10.1016/j.jmmm.2003.08.005 · Cited by 11

Stochasticity enhances the gaining of bet-hedging strategies in contact-process-like dynamics

Hidalgo, J., Simone Pigolotti, A., & Muñoz, M. A. (2015) · Physical Review E · doi:10.1103/physreve.91.032114 · Cited by 11

Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method

Gross, M., & Varnik, F. (2012) · Physical Review E · doi:10.1103/physreve.85.056707 · Cited by 12

Introduction to Simulation Techniques

Janke, W. (2007) · Lecture notes in physics · doi:10.1007/3-540-69684-9_5 · Cited by 11

Existence of radial solutions to biharmonic k-Hessian equations

Escudero, C., & Torres, P. J. (2015) · Journal of Differential Equations · doi:10.1016/j.jde.2015.04.001 · Cited by 11

Phase transitions in physiologically-based multiscale mean-field brain models

Robinson, P. A., RENNIE, C. J., Phillips, A. J. K., Kim, J. W., & Roberts, J. A. (2009) · Springer eBooks · doi:10.1007/978-1-4419-0796-7_8 · Cited by 11

From Ginzburg–Landau to Hilbert–Einstein via Yamabe

Kholodenko, A. L., & Ballard, E. E. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.02.053 · Cited by 11

Structure, dynamics and spectroscopy of single molecules: A challenge to quantum mechanics

Amann, A. (1995) · Journal of Mathematical Chemistry · doi:10.1007/bf01164662 · Cited by 11

The glass transition in terms of Landau’s phenomenological approach

Gutzow, I. S., & Petroff, B. P. (2004) · Journal of Non-Crystalline Solids · doi:10.1016/j.jnoncrysol.2004.08.079 · Cited by 11

Anomalous scaling in homogeneous isotropic turbulencePreprint

Giles, M. J., & Revtex, T. U. (2000) · Cited by 11

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

Kapcia, K. J. (2021) · Nanomaterials · doi:10.3390/nano11051181 · Cited by 10

Stochastic Multiscale Models of Cell Population Dynamics: Asymptotic and Numerical Methods

Guerrero, P., & Alarcón, T. (2015) · Mathematical Modelling of Natural Phenomena · doi:10.1051/mmnp/201510104 · Cited by 10

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

Suzuki, O., & Zhi-dong, Z. (2021) · Mathematics · doi:10.3390/math9070776 · Cited by 10

The Mean Field Approach for Populations of Spiking Neurons

Camera, G. L. (2021) · Advances in experimental medicine and biology · doi:10.1007/978-3-030-89439-9_6 · Cited by 9

Field equation of the correlation function of mass-density fluctuations for self-gravitating systems

Zhang, Y., & Chen, Q. (2015) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201425431 · Cited by 10

Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density

Mendonça, J. R. G. (2011) · Physical Review E · doi:10.1103/physreve.83.031112 · Cited by 10

Inferring planar disorder in close-packed structuresvia∊-machine spectral reconstruction theory: examples from simulated diffraction patterns

Varn, D. P., Canright, G., & Crutchfield, J. P. (2013) · Acta Crystallographica Section A Foundations of Crystallography · doi:10.1107/s0108767313008738 · Cited by 9

Phase transitions and critical phenomena

Nishimori, H., & Ortiz, G. E. (2010) · doi:10.1093/acprof:oso/9780199577224.003.0001 · Cited by 10

Field-induced incommensurate ordering in Heisenberg chains coupled by Ising interaction: Model for ytterbium aluminum perovskite YbAlO3

Agrapidis, C. E., van den Brink, J., & Nishimoto, S. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.224423 · Cited by 10

Electron pairing in mirror modes: surpassing the quasi-linear limit

Treumann, R. A., & Baumjohann, W. (2019) · Annales Geophysicae · doi:10.5194/angeo-37-971-2019 · Cited by 10

Super slowing down in the bond-diluted Ising model

Zhong, W., Barkema, G. T., & Panja, D. (2020) · Physical review. E · doi:10.1103/physreve.102.022132 · Cited by 10

Onset of criticality in hyper-auxetic polymer networks

Ninarello, A., Ruiz‐Franco, J., & Zaccarelli, E. (2022) · Nature Communications · doi:10.1038/s41467-022-28026-z · Cited by 10

Spectral signatures of symmetry-breaking dynamical phase transitions

Hurtado-Gutiérrez, R., Hurtado, P. I., & Pérez-Espigares, C. (2023) · Physical review. E · doi:10.1103/physreve.108.014107 · Cited by 10

Small angle neutron scattering studies of a polybutadiene/polystyrene blend with small additions of ortho-dichloro-benzene for varying temperatures and pressures. I. Mean field to 3D-Ising crossover behavior

Schwahn, D., Frielinghaus, H., & Willner, L. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1429959 · Cited by 10

One-dimensional behavior of ferroelastic domain arrays in neodymium pentaphosphate

Huang, X. R., Jiang, S., Hu, X., et al. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.9932 · Cited by 10

Resonant RHEED measurements of surface order on Cu3Au(111) films

Bonham, S. W., & Flynn, C. P. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.57.4099 · Cited by 10

Onset of self-assembly

Chitanvis, S. M. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.1921 · Cited by 10

Droplet vaporization at critical conditions: Long-time convective-diffusive profiles along the critical isobar

Arias‐Zugasti, M., García‐Ybarra, P. L., & Castillo, J. L. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.60.2930 · Cited by 10

SYSTEMIC LUPUS ERYTHEMATOSUS IN AFRICAN-AMERICAN WOMEN: COGNITIVE PHYSIOLOGICAL MODULES, AUTOIMMUNE DISEASE, AND STRUCTURED PSYCHOSOCIAL STRESS

Wallace, R. (2003) · Advances in Complex Systems · doi:10.1142/s0219525903001092 · Cited by 11

Temperature induced phase transformations of molecular nanoclusters

Proykova, A., Pisov, S., Radev, R., et al. (2002) · Vacuum · doi:10.1016/s0042-207x(02)00291-9 · Cited by 10

Crossover model for the work of critical cluster formation in nucleation theory

Kalikmanov, V. I. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1806404 · Cited by 10

Is anything ever new?: considering emergence

Crutchfield, J. P. (1999) · Cited by 10

Roughening transition in the presence of adsorbates

Vakarin, E. V., & Badiali, J. P. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.60.2064 · Cited by 10

Ising Model Scaling Behaviour on z-Preserving Small-World NetworksPreprint

Hawick, K. A., & James, H. A. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0611763 · Cited by 10

Comorbidity and Anticomorbidity: Autocognitive developmental disorders of structured psychosocial stressPreprint

Wallace, R. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.q-bio/0310001 · Cited by 9

Mean field phase diagrams for one-electron molecules

Serra, P., & Kais, S. (1997) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/30/5/016 · Cited by 10

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

Mihailović, D. T., Mimić, G., Nikolić-Ðorić, E., et al. (2014) · Open Physics · doi:10.1515/phys-2015-0001 · Cited by 9

Multi-scale Laplacian community detection in heterogeneous networks

Villegas, P., Gabrielli, A., Poggialini, A., & Gili, T. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013065 · Cited by 10

Piezoelectric strain induced variation of the magnetic anisotropy in a high Curie temperature (Ga,Mn)As sample

Casiraghi, A., Rushforth, A. W., Zemen, J., et al. (2012) · Applied Physics Letters · doi:10.1063/1.4746250 · Cited by 9

Modeling large Mexican urban metropolitan areas by a Vicsek Szalay approach

Murcio, R., & Rodríguez‐Romo, S. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.04.002 · Cited by 9

Nematic phase in two-dimensional frustrated systems with power-law decaying interactions

Barci, D. G., Ribeiro, L., & Stariolo, D. A. (2013) · Physical Review E · doi:10.1103/physreve.87.062119 · Cited by 9

Universality Reduced

Franklin, A. (2019) · Philosophy of Science · doi:10.1086/705473 · Cited by 9

Consistency of potential energy in the dynamical vertex approximation

Stobbe, J., & Rohringer, G. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.205101 · Cited by 9

Critical Behaviour in Ferroelectrics as Studied by Nonlinear Dielectric Effect. Invariants of the Electric Susceptibility in a Biasing Field

Gałązka, M., Szklarz, P., Bator, G., et al. (2006) · Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena · doi:10.4028/www.scientific.net/ssp.112.141 · Cited by 9

Phase behavior of the confined Lebwohl-Lasher model

Almarza, N. G., Martín, C., & Lomba, E. (2010) · Physical Review E · doi:10.1103/physreve.82.011140 · Cited by 9

Living poly(α-methylstyrene) near the polymerization line: VIII. Mass density, viscosity, and surface tension in tetrahydrofuran

Pendyala, K. S., Gu, X., Andrews, K. P., et al. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1346636 · Cited by 9

A Study on Transient Changes of Surface Morphologies in Ag and Sb Coelectrodeposition

SAITOU, M., & Fukuoka, Y. (2004) · Journal of The Electrochemical Society · doi:10.1149/1.1787499 · Cited by 9

Breakup of Universality in the Generalized Spinodal Nucleation Theory

Muratov, C. B., & Vanden‐Eijnden, E. (2004) · Journal of Statistical Physics · doi:10.1023/b:joss.0000012504.46631.89 · Cited by 9

Field equation of the correlation function of mass-density fluctuations for self-gravitating systems

Zhang, Y., & Chen, Q. (2015) · Springer Link (Chiba Institute of Technology) · doi:10.1051/0004-6361/201425431/pdf · Cited by 9

The A-B Diblock Copolymer as a Nonordering External Field in a Three-Component A/B/A-B Polymer Blend

Pipich, V., Willner, L., & Schwahn, D. (2008) · The Journal of Physical Chemistry B · doi:10.1021/jp805903p · Cited by 9

Modeling the Critical and Phase Equilibrium Properties of Pure Fluids and Mixtures with the Crossover Cubic-Plus-Association Equation of State

Vinhal, A. P. C. M., Yan, W. J., & Kontogeorgis, G. M. (2019) · Journal of Chemical & Engineering Data · doi:10.1021/acs.jced.9b00492 · Cited by 9

Anomalous dimension exponents on fractal structures for the Ising and three-state Potts model

Monceau, P., & Hsiao, P. (2002) · Physics Letters A · doi:10.1016/s0375-9601(02)00898-8 · Cited by 9

Renormalization schemes for earthquake prediction

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Critical exponents of SU(2) gauge theory in 2+1 dimensions

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CRITICAL EXPONENTS AND CRITICAL SLOWING DOWN IN OPTICAL BISTABILITY — A PHENOMENOLOGICAL APPROACH

Tsao, P.-H., & Liu, W.-C. (1992) · Modern Physics Letters B · doi:10.1142/s0217984992000442 · Cited by 1

Critical Exponents of O(N) Scalar Model at Temperatures below the Critical Value Using Auxiliary Mass Method

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Divergence behavior of thermodynamic curvature scalar at critical point in the extended phase space of generic black holes

Hu, Y.-P., Cai, L. J., Liang, X. G., et al. (2021) · Physics Letters B · doi:10.1016/j.physletb.2021.136661 · Cited by 17

Critical phenomena in constrained systems and random-field problem

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