Antiferromagnetism
Abstract
The ground state of a lattice with one electron per atom and antiferromagnetic interactions between nearest neighbours only is examined by a variational method similar in principle to the treatments by Hulthén (1938) and Kasteleijn (1952) of the linear-chain problem. The calculation involves a statistical problem which is shown to be exactly equivalent to the Ising ferromagnetic problem. This cannot be solved exactly, except in the one-dimensional case, and so the Bethe–Peierls method is used to solve it approximately. In complete contradiction to the Kubo (1953) variational calculation it is concluded that all lattices have disordered ground states. The energy differences between ordered and disordered states are small and so the nature of the ground state is likely to be sensitive to small additional ordering forces.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Based on Marshall's theorem and its extension, the absolute ground state has total spin zero for N spins on a bipartite lattice with nearest-neighbor antiferromagnetic Heisenberg-type interactions.
“Based on Marshall's theorem[35] and its extension[36] the absolute ground state has total spin zero ( S 2 = 0 ) for N spins on a bipartite lattice with nearest-neighbor antiferromagnetic Heisenberg-type interactions.”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [35]
Cites
Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet
Holstein, T. D., & Primakoff, H. (1940) · Physical Review · doi:10.1103/physrev.58.1098 · Cited by 4,063 · see citing works
Beitrag zur Theorie des Ferromagnetismus
Ising, E. (1925) · Zeitschrift für Physik · doi:10.1007/bf02980577 · Cited by 3,871 · see citing works
An Approximate Quantum Theory of the Antiferromagnetic Ground State
Anderson, P. W. (1952) · Physical Review · doi:10.1103/physrev.86.694 · Cited by 1,337 · see citing works
The Spin-Wave Theory of Antiferromagnetics
Kubo, R. (1952) · Physical Review · doi:10.1103/physrev.87.568 · Cited by 724 · see citing works
Limits on the Energy of the Antiferromagnetic Ground State
Anderson, P. W. (1951) · Physical Review · doi:10.1103/physrev.83.1260 · Cited by 151 · see citing works
Antiferromagnetism by the Spin Wave Method I: The Energy Levels
Ziman, J. M. (1952) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/65/7/309 · Cited by 70 · see citing works
The lowest energy state of a linear antiferromagnetic chain
Kasteleijn, P. W. (1952) · Physica · doi:10.1016/s0031-8914(52)80273-3 · Cited by 68 · see citing works
The Spin-Wave Theory as a Variational Method and Its Application to Antiferromagnetism
Kubo, R. (1953) · Reviews of Modern Physics · doi:10.1103/revmodphys.25.344 · Cited by 61 · see citing works
Lidiard, A. B. (1954) · Reports on Progress in Physics · doi:10.1088/0034-4885/17/1/307 · Cited by 61 · see citing works
Antiferromagnetism by the Spin Wave Method III: Application to more Complex Systems
Ziman, J. M. (1953) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/66/1/313 · Cited by 28 · see citing works
Antiferromagnetism by the Spin Wave Method II: Magnetic Properties
Ziman, J. M. (1952) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/65/7/310 · Cited by 21 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Linear Magnetic Chains with Anisotropic Coupling
Bonner, J. C., & Fisher, M. E. (1964) · Physical Review · doi:10.1103/physrev.135.a640 · Cited by 2,497 · see citing works
Zhou, Y., Kanoda, K., & Ng, T. K. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.025003 · Cited by 1,464 · see citing works
The spin-½ Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides
Manousakis, E. (1991) · Reviews of Modern Physics · doi:10.1103/revmodphys.63.1 · Cited by 1,252 · see citing works
Aspuru-Guzik, A., & Walther, P. (2012) · Nature Physics · doi:10.1038/nphys2253 · Cited by 952 · see citing works
“In addition to the superior level of quantum control, photonic quantum simulators allow the use of quantum interference at beamsplitters which can lead to interesting photon-entanglement that corresponds to ground states of correlated chemical or solid-state systems 56 .”
Exact solution of an S =1/2 Heisenberg antiferromagnetic chain with long-ranged interactions
Shastry, B. S. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.639 · Cited by 769 · see citing works
Electrons in transition metals
Mott, N. F. (1964) · Advances In Physics · doi:10.1080/00018736400101041 · Cited by 697 · see citing works
Simple Variational Wave Functions for Two-Dimensional Heisenberg Spin-½ Antiferromagnets
Huse, D. A., & Elser, V. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.2531 · Cited by 563 · see citing works
Linear Antiferromagnetic Chain with Anisotropic Coupling
Orbach, R. (1958) · Physical Review · doi:10.1103/physrev.112.309 · Cited by 532 · see citing works
Liang, S., Douçot, B., & Anderson, P. W. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.365 · Cited by 519 · see citing works
Mobile Vacancies in a Quantum Heisenberg Antiferromagnet
Shraiman, B. I., & Siggia, E. D. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.467 · Cited by 420 · see citing works
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
Sorella, S., Otsuka, Y., & Yunoki, S. (2012) · Scientific Reports · doi:10.1038/srep00992 · Cited by 327 · see citing works
Antiferromagnetic model with known ground state
Majumdar, C. K. (1970) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/3/4/019 · Cited by 277 · see citing works
Gutzwiller projection for bosons
Rokhsar, D. S., & Kotliar, B. G. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.44.10328 · Cited by 263 · see citing works
Evidence for Itinerant d -Electron Ferromagnetism
Jarrett, H. S., Cloud, W. H., Bouchard, R. J., BUTLER, S. R., Frederick, C. G., & Gillson, J. L. (1968) · Physical Review Letters · doi:10.1103/physrevlett.21.617 · Cited by 260 · see citing works
Statistics of the excitations of the resonating-valence-bond state
Read, N., & Chakraborty, B. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.40.7133 · Cited by 249 · see citing works
Ground-state correlations of quantum antiferromagnets: A Green-function Monte Carlo study
Trivedi, N., & Ceperley, D. M. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.41.4552 · Cited by 238 · see citing works
Two-dimensional frustrated J1−J2 model studied with neural network quantum states
Choo, K., Neupert, T., & Carleo, G. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.125124 · Cited by 238 · see citing works
Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
Yunoki, S., & Sorella, S. (2006) · Physical Review B · doi:10.1103/physrevb.74.014408 · Cited by 214 · see citing works
Pati, S. K., Ramasesha, S., & Sen, D. (1997) · Physical review. B, Condensed matter · doi:10.1103/physrevb.55.8894 · Cited by 191 · see citing works
Edegger, B., Muthukumar, V. N., & Gros, C. (2007) · Advances In Physics · doi:10.1080/00018730701627707 · Cited by 189 · see citing works
Effects of frustration on magnetic molecules: a survey from Olivier Kahn until today
Schnack, J. (2010) · Dalton Transactions · doi:10.1039/b925358k · Cited by 188 · see citing works
Theory of the spin liquid state of the Heisenberg antiferromagnet
Kalmeyer, V., & Laughlin, R. B. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.39.11879 · Cited by 186 · see citing works
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems
Ma, X.-S., Dakic, B., Naylor, W., Zeilinger, A., & Walther, P. (2011) · Nature Physics · doi:10.1038/nphys1919 · Cited by 179 · see citing works
Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain
Bursill, R., Gehring, G. A., FARNELL, D. J. J., Parkinson, J. B., Xiang, T., & Zeng, C. (1995) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/7/45/016 · Cited by 178 · see citing works
Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
Richter, J., Schulenburg, J., & Honecker, A. (2004) · Lecture notes in physics · doi:10.1007/bfb0119592 · Cited by 161 · see citing works
The Resonating Valence Bond State in La2CuO4and Superconductivity
Anderson, P. W. (1993) · Perspectives in condensed matter physics · doi:10.1007/978-94-011-1622-0_35 · Cited by 207 · see citing works
Systems with resonating-valence-bond ground states: Correlations and excitations
Sutherland, B. (1988) · Physical review. B, Condensed matter · doi:10.1103/physrevb.37.3786 · Cited by 155 · see citing works
Yokoyama, H., & Shiba, H. (1987) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.56.3570 · Cited by 155 · see citing works
Reexamination of entanglement and the quantum phase transition
Yang, M.-F. (2005) · Physical Review A · doi:10.1103/physreva.71.030302 · Cited by 149 · see citing works
Finite-lattice extrapolations for a Haldane-gap antiferromagnet
Golinelli, O., Jolicœur, T., & Lacaze, R. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.50.3037 · Cited by 142 · see citing works
Square-lattice Heisenberg antiferromagnet atT=0
Weihong, Z., Oitmaa, J., & Hamer, C. J. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.8321 · Cited by 141 · see citing works
Exact diagonalization of finite frustrated spin-(1/2 Heisenberg models
Figueirido, F. E., Karlhede, A., Kivelson, S. A., Sondhi, S. L., Martin Roček, B., & Rokhsar, D. S. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.41.4619 · Cited by 137 · see citing works
Phase string effect in the t-J model: General theory
Weng, Z.-Y., Sheng, D. N., Chen, Y.-C., & Ting, C. S. (1997) · Physical review. B, Condensed matter · doi:10.1103/physrevb.55.3894 · Cited by 123 · see citing works
Neural network wave functions and the sign problem
Szabó, A., & Castelnovo, C. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033075 · Cited by 119 · see citing works
Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain
Bursill, R., Gehring, G. A., FARNELL, D. J. J., Parkinson, J. B., Xiang, T., & Zeng, C. (1995) · Research Explorer (The University of Manchester) · Cited by 110 · see citing works
Spencer, J. S., Blunt, N. S., & Foulkes, W. M. C. (2012) · The Journal of Chemical Physics · doi:10.1063/1.3681396 · Cited by 104 · see citing works
Class of variational singlet wave functions for the Hubbard model away from half filling
Anderson, P. W., Shastry, B. S., & Hristopulos, D. T. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.40.8939 · Cited by 108 · see citing works
Phase String Effect in a Doped Antiferromagnet
Sheng, D. N., Chen, Y. C., & Weng, Z.-Y. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.5102 · Cited by 107 · see citing works
Doped antiferromagnet: The instability of homogeneous magnetic phases
Auerbach, A., & Larson, B. E. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.7800 · Cited by 104 · see citing works
Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries
Vieijra, T., Casert, C., Nys, J., Neve, W. D., Haegeman, J., Ryckebusch, J., & Verstraete, F. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.097201 · Cited by 102 · see citing works
Statistics of holons in the quantum hard-core dimer gas
Kivelson, S. A. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.39.259 · Cited by 100 · see citing works
Monte Carlo calculations of the correlation functions for Heisenberg spin chains atT=0
Liang, S. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1597 · Cited by 101 · see citing works
Ground-state and low-lying excitations of the Heisenberg antiferromagnet
Carlson, J. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.40.846 · Cited by 101 · see citing works
Properties of the chiral-spin-liquid state
Laughlin, R. B., & Zou, Z. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.41.664 · Cited by 100 · see citing works
Antiferromagnetic Linear Chain
Mattheiss, L. F. (1961) · Physical Review · doi:10.1103/physrev.123.1209 · Cited by 99 · see citing works
Fermion-spin transformation to implement the charge-spin separation
Feng, S., Su, Z., & Yu, L. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.49.2368 · Cited by 98 · see citing works
New Method for Treating the Antiferromagnetic Ground State
Davis, H. L. (1960) · Physical Review · doi:10.1103/physrev.120.789 · Cited by 94 · see citing works
Neural Gutzwiller-projected variational wave functions
Ferrari, F., Becca, F., & Carrasquilla, J. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.125131 · Cited by 93 · see citing works
Singlet ground state of the periodic Anderson model at half filling: A rigorous result
Ueda, K., Tsunetsugu, H., & Sigrist, M. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.1030 · Cited by 93 · see citing works
Empowering deep neural quantum states through efficient optimization
Chen, A., & Heyl, M. (2024) · Nature Physics · doi:10.1038/s41567-024-02566-1 · Cited by 92 · see citing works
Symmetry breaking and finite-size effects in quantum many-body systems
Koma, T., & Tasaki, H. (1994) · Journal of Statistical Physics · doi:10.1007/bf02188685 · Cited by 88 · see citing works
Characterization of Topological Insulators: Chern Numbers for Ground State Multiplet
Hatsugai, Y. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.1374 · Cited by 86 · see citing works
Phase transitions in the spin-half J1−J2 model
Bishop, R. F., FARNELL, D. J. J., & Parkinson, J. B. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.58.6394 · Cited by 86 · see citing works
Ground-state features for Heisenberg models
Klein, D. (1982) · The Journal of Chemical Physics · doi:10.1063/1.444232 · Cited by 85 · see citing works
Existence of Néel order atT=0 in the spin-1/2 antiferromagnetic Heisenberg model on a square lattice
Liang, S. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.42.6555 · Cited by 84 · see citing works
Symmetry-adapted variational quantum eigensolver
Seki, K., Shirakawa, T., & Yunoki, S. (2020) · Physical Review A · doi:10.1103/physreva.101.052340 · Cited by 81 · see citing works
Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations
Wang, L., Liu, Y.-H., Iazzi, M., Troyer, M., & Harcos, G. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.250601 · Cited by 78 · see citing works
Some formal results for the valence bond basis
Beach, K. S. D., & Sandvik, A. W. (2006) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2006.05.032 · Cited by 80 · see citing works
Metallic and non-metallic behaviour in compounds of transition metals
Mott, N. F. (1969) · Philosophical magazine · doi:10.1080/14786436908228532 · Cited by 78 · see citing works
Finite-size effects on the optical conductivity of a half-filled Hubbard ring
Stafford, C. A., Millis, A. J., & Shastry, B. S. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.13660 · Cited by 78 · see citing works
Magnetic order in a spin- 1 2 interpolating square-triangle Heisenberg antiferromagnet
Bishop, R. F., Li, P. H. Y., FARNELL, D. J. J., & Campbell, C. E. (2009) · Physical Review B · doi:10.1103/physrevb.79.174405 · Cited by 75 · see citing works
Tetrahis(dimethylamino)ethylene- C60 : Multicomponent superexchange and Mott ferromagnetism
Arovas, D. P., & Auerbach, A. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.10114 · Cited by 75 · see citing works
Thermodynamic Properties of Spin 1/2 Antiferromagnetic Heisenberg Model on the Square Lattice
Miyashita, S. (1988) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.57.1934 · Cited by 71 · see citing works
Properties of resonating-valence-bond spin liquids and critical dimer models
Tang, Y., Sandvik, A. W., & Henley, C. L. (2011) · Physical Review B · doi:10.1103/physrevb.84.174427 · Cited by 69 · see citing works
Bukov, M., Schmitt, M., & Dupont, M. (2021) · eScholarship (California Digital Library) · Cited by 73 · see citing works
Frustration Effect in Quantum Spin Systems
Marland, L. G., & Betts, D. D. (1979) · Physical Review Letters · doi:10.1103/physrevlett.43.1618 · Cited by 68 · see citing works
Bukov, M., Schmitt, M., & Dupont, M. (2021) · SciPost Physics · doi:10.21468/scipostphys.10.6.147 · Cited by 66 · see citing works
Effects of cyclic four-spin exchange on the magnetic properties of the CuO2 plane
Honda, Y., Kuramoto, Y., & Watanabe, T. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.47.11329 · Cited by 66 · see citing works
Ground-State Energy of the Heisenberg Model with XY-Like Anisotropy
Nishimori, H., & Miyake, S. J. (1985) · Progress of Theoretical Physics · doi:10.1143/ptp.73.18 · Cited by 66 · see citing works
Valence Bond Entanglement Entropy
Alet, F., Capponi, S., Laflorencie, N., & Mambrini, M. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.117204 · Cited by 66 · see citing works
Richter, J., Ivanov, N. B., & Retzlaff, K. (1994) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/25/7/012 · Cited by 63 · see citing works
Two-dimensional Heisenberg antiferromagnet: A numerical study
Barnes, T., & Swanson, E. S. (1988) · Physical review. B, Condensed matter · doi:10.1103/physrevb.37.9405 · Cited by 63 · see citing works
Gapped spin-liquid phase in the J1−J2 Heisenberg model by a bosonic resonating valence-bond ansatz
Li, T., Becca, F., Hu, W.-J., & Sorella, S. (2012) · Physical Review B · doi:10.1103/physrevb.86.075111 · Cited by 62 · see citing works
Correlation amplitude and entanglement entropy in random spin chains
Hoyos, J. A., Vieira, A. P., Laflorencie, N., & Miranda, E. (2007) · Physical Review B · doi:10.1103/physrevb.76.174425 · Cited by 61 · see citing works
Simplex solid states of SU(N) quantum antiferromagnets
Arovas, D. P. (2008) · Physical Review B · doi:10.1103/physrevb.77.104404 · Cited by 59 · see citing works
Sign structure of the t−J model
Wu, K., Weng, Z.-Y., & Zaanen, J. (2008) · Physical Review B · doi:10.1103/physrevb.77.155102 · Cited by 58 · see citing works
Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet
Chayes, J., Chayes, L., & Kivelson, S. A. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01244017 · Cited by 58 · see citing works
High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
Roth, C., Szabó, A., & MacDonald, A. H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.054410 · Cited by 58 · see citing works
Antiferromagnetic Magnon Dispersion Law and Bloch Wall Energies in Ferromagnets and Antiferromagnets
Orbach, R. (1959) · Physical Review · doi:10.1103/physrev.115.1181 · Cited by 56 · see citing works
Linear Antiferromagnetic Chain
Rodríguez, S. (1959) · Physical Review · doi:10.1103/physrev.116.1474 · Cited by 56 · see citing works
Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings
Bärwinkel, K., Hage, P., Schmidt, H., & Schnack, J. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.054422 · Cited by 53 · see citing works
Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study
Kaxiras, E., & Manousakis, E. (1988) · Physical review. B, Condensed matter · doi:10.1103/physrevb.37.656 · Cited by 53 · see citing works
Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems 1Preprint
Koma, T., & Tasaki, H. (1997) · Cited by 51 · see citing works
Kinetic-energy-driven superconductivity in cuprate superconductors
Feng, S., Lan, Y., Zhao, H., Kuang, L., Qin, L., & Ma, X. (2015) · International Journal of Modern Physics B · doi:10.1142/s0217979215300091 · Cited by 50 · see citing works
Binding of holes and the pair spectral function in thet-Jmodel
Poilblanc, D. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.3368 · Cited by 49 · see citing works
Speeding Up Learning Quantum States Through Group Equivariant Convolutional Quantum Ansätze
Zheng, H., Li, Z., Liu, J., Strelchuk, S., & Kondor, R. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.020327 · Cited by 51 · see citing works
Solution of the time-dependent Schrödinger equation for two-dimensional spin-1/2 Heisenberg systems
de Vries, P., & Raedt, H. A. D. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.47.7929 · Cited by 48 · see citing works
Ground-state properties of antiferromagnetic Heisenberg spin rings
Bärwinkel, K., Schmidt, H., & Schnack, J. (2000) · Journal of Magnetism and Magnetic Materials · doi:10.1016/s0304-8853(00)00481-9 · Cited by 47 · see citing works
Richter, J., Ivanov, N. B., & Schulenburg, J. (1998) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/10/16/015 · Cited by 47 · see citing works
New Variational Method for the Antiferromagnetic Ground State
Bartkowski, R. (1972) · Physical review. B, Solid state · doi:10.1103/physrevb.5.4536 · Cited by 47 · see citing works
Large magnetic molecules and what we learn from them
Schnack, J. (2019) · Contemporary Physics · doi:10.1080/00107514.2019.1615716 · Cited by 43 · see citing works
Phase diagram of S=12 two-leg XXZ spin-ladder systems
Hijii, K., Kitazawa, A., & Nomura, K. (2005) · Physical Review B · doi:10.1103/physrevb.72.014449 · Cited by 46 · see citing works
Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J 1 - J 2 model
Bishop, R. F., Li, P. H. Y., FARNELL, D. J. J., Richter, J., & Campbell, C. E. (2012) · Physical Review B · doi:10.1103/physrevb.85.205122 · Cited by 45 · see citing works
Entanglement in the Majumdar-Ghosh model
Chhajlany, R. W., Tomczak, P., Wójcik, A., & Richter, J. (2007) · Physical Review A · doi:10.1103/physreva.75.032340 · Cited by 45 · see citing works
The coupled cluster method applied to quantum magnetism
FARNELL, D. J. J., & Bishop, R. F. (2004) · Lecture notes in physics · doi:10.1007/bfb0119597 · Cited by 45 · see citing works
de Jongh, M. S. L. D. C., van Leeuwen, J. M. J., & van Saarloos, W. (2000) · Physical review. B, Condensed matter · doi:10.1103/physrevb.62.14844 · Cited by 45 · see citing works
On the description of the antiferromagnetism without anomalous averages
Irkhin, V. Y., & Katsnelson, M. I. (1986) · The European Physical Journal B · doi:10.1007/bf01323431 · Cited by 44 · see citing works
Nakano, H., & Sakai, T. (2014) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.83.104710 · Cited by 44 · see citing works
Spin- 12J1−J2 model on the body-centered cubic lattice
Schmidt, R., Schulenburg, J., Richter, J., & Betts, D. D. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.66.224406 · Cited by 44 · see citing works
Superconducting ground state of a doped Mott insulator
Weng, Z.-Y. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/10/103039 · Cited by 43 · see citing works
- Authors
- Marshall, W.
- Affiliations
- University of Birmingham (GB)
- Corresponding author
- Marshall, W.
- Venue
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1955-10-11
- Volume
- 232
- Issue
- 1188
- Pages
- 48-68
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W4250463753
- Cited by
- 444
- References
- 11
- Citations by year
- 2026: 8 · 2025: 17 · 2024: 13 · 2023: 15 · 2022: 12 · 2021: 15 · 2020: 15 · 2019: 11 · 2018: 13 · 2017: 9 · 2016: 8 · 2015: 12 · 2014: 13 · 2013: 7 · 2012: 11
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- antiferromagnetism, ground state, Ising model, variational methods, disordered ground state, lattice spin systems
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
