摘要: An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit spontaneous magnetization at temperatures above the mean-field approximation Curie or “critical” point. (As consequence, corresponding “lattice gas” undergo first order phase transition in density (condensation) this temperature.) The susceptibility zero magnetic field high shown be upper bound exact result.
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sci-hub.se 参考文章(7)
Robert B. Griffiths, Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising Ferromagnet Physical Review. ,vol. 136, pp. A437- A439 ,(1964) , 10.1103/PHYSREV.136.A437
T. D. Lee, C. N. Yang, Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model Physical Review. ,vol. 87, pp. 410- 419 ,(1952) , 10.1103/PHYSREV.87.410
M. Kac, C. J. Thompson, ON THE MATHEMATICAL MECHANISM OF PHASE TRANSITION Proceedings of the National Academy of Sciences of the United States of America. ,vol. 55, pp. 676- 683 ,(1966) , 10.1073/PNAS.55.4.676
T. D. SCHULTZ, D. C. MATTIS, E. H. LIEB, Two-Dimensional Ising Model as a Soluble Problem of Many Fermions Reviews of Modern Physics. ,vol. 36, pp. 856- 871 ,(1964) , 10.1103/REVMODPHYS.36.856
Lars Onsager, Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition Physical Review. ,vol. 65, pp. 117- 149 ,(1944) , 10.1103/PHYSREV.65.117
Michael E. Fisher, Correlation Functions and the Coexistence of Phases Journal of Mathematical Physics. ,vol. 6, pp. 1643- 1653 ,(1965) , 10.1063/1.1704706
R. Peierls, On Ising's model of ferromagnetism Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 32, pp. 477- 481 ,(1936) , 10.1017/S0305004100019174