Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

Phys. Rev. 87, 410 – Published 1 August 1952
T. D. Lee and C. N. Yang

Abstract

The problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent. From this equivalence an example of a two-dimensional lattice gas is given for which the phase transition regions in the p-v diagram is exactly calculated.

A theorem is proved which states that under a class of general conditions the roots of the grand partition function always lie on a circle. Consequences of this theorem and its relation with practical approximation methods are discussed. All the known exact results about the two-dimensional square Ising lattice are summarized, and some new results are quoted.

DOI: http://dx.doi.org/10.1103/PhysRev.87.410

  • Received 31 March 1952
  • Published in the issue dated August 1952

© 1952 The American Physical Society

Authors & Affiliations

T. D. Lee and C. N. Yang

  • Institute for Advanced Study, Princeton, New Jersey

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