Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
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.
- Publication:
-
Physical Review
- Pub Date:
- August 1952
- DOI:
- 10.1103/PhysRev.87.410
- Bibcode:
- 1952PhRv...87..410L