Abstract
Another possible method for obtaining Onsager’s solution for the 2D Ising model is presented. In contrast to previous methods, the method proposed here makes it possible to study the problem in a weak external magnetic field. Generalized Jordan-Wigner transformations in the form introduced by Kochmański [J. Tech. Phys. 36, 485 (1995)] are employed.
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References
M. S. Kochmański, J. Tech. Phys. 36, 485 (1995).
B. McCoy and T. T. Wu, Two-Dimensional Ising Models, Harvard University Press, Cambridge (1973).
J. M. Ziman, Models of Disorder, Cambridge University Press, New York (1979).
R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, New York (1982).
Yu. A. Izyumov and Yu. N. Skryabin, Statistical Mechanics of Magnetically Ordered Systems, Consultants Bureau, New York (1988).
C. J. Thompson, Classical Equilibrium Statistical Mechanics, Clarendon Press, Oxford (1988).
T. D. Schultz, D. C. Mattis, and E. H. Lieb, Rev. Mod. Phys. 36, 856 (1964).
P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928).
M. Kac and J. C. Ward, Phys. Rev. 88, 1332 (1952).
P. W. Kasteleyn, J. Math. Phys. 4, 287 (1963).
N. V. Vdovichenko, Zh. Éksp. Teor. Fiz. 47, 715 (1964) [Sov. Phys. JETP 20, 477 (1965)].
R. J. Baxter and I. G. Enting, J. Phys. A 11, 2463 (1978).
M. S. Kochmański, submitted to Phys. Rev. E.
L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon Press, New York (1977).
F. Harary (ed.). Graph Theory and Theoretical Physics, Academic Press, New York (1967).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York (1973).
W. T. Tutte, Graph Theory, Cambridge University Press, New York (1984).
G. C. Wick, Phys. Rev. 80, 268 (1950).
C. A. Hurst and H. S. Green, J. Chem. Phys. 33, 1059 (1961).
M. S. Kochmański, J. Tech. Phys. 37, 67 (1996).
M. S. Kochmański, submitted to Ann. Polon. Math. (1996).
R. P. Feynman, Statistical Mechanics, W. A. Benjamin, Inc., Reading, Massachusetts (1972).
S. Sherman, J. Math. Phys. 1, 202 (1960); ibid. 4, 1213 (1963).
L. D. Landau and E. M. Lifshitz, Statistical Physics, Pergamon Press, New York (1980).
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Zh. Éksp. Teor. Fiz. 111, 1717–1731 (May 1997)
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Kochmański, M.S. Generalized Jordan-Wigner transformations and the Ising-Onsager problem. J. Exp. Theor. Phys. 84, 940–947 (1997). https://doi.org/10.1134/1.558232
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DOI: https://doi.org/10.1134/1.558232