General Lattice Model of Phase Transitions

Chungpeng Fan and F. Y. Wu
Phys. Rev. B 2, 723 – Published 1 August 1970
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Abstract

A general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed. Besides the well-known Ising and "ice" models, other soluble cases are also considered. After discussing some general symmetry properties of this model, we consider in detail a particular class of the soluble cases, the "free-fermion" model. The explicit expressions for all thermodynamic functions with the inclusion of an external electric field are obtained. It is shown that both the specific heat and the polarizability of the free-fermion model exhibit in general a logarithmic singularity. An inverse-square-root singularity results, however, if the free-fermion model also satisfies the ice condition. The results are illustrated with a specific example.

  • Received 16 December 1969

DOI:https://doi.org/10.1103/PhysRevB.2.723

©1970 American Physical Society

Authors & Affiliations

Chungpeng Fan

  • Department of Physics, Rutgers, The State University, New Brunswick, New Jersey 08903

F. Y. Wu*

  • Department of Physics, Northeastern University, Boston, Massachusetts 02115

  • *Work supported in part by National Science Foundation Grant No. GP-9041.

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Issue

Vol. 2, Iss. 3 — 1 August 1970

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