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 twodimensional lattice gas is given for which the phase transition regions in the pv 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 twodimensional 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