PHASE-TRANSITIONS IN AN ASYMMETRICAL ISING-MODEL

An asymmetrical Ising model in which the eigenvalues of the operators Sz and (Sz)2 are 1,0, and 1, 0, 2 (being a parameter: 0<1) respectively is studied using Bragg-Williams approximation. It is shown that such an asymmetrical model is equivalent to a symmetrical model with renormalized coupling constants. The corresponding lattice-gas model is proposed which introduces four coupled ordering parameters: m= qM=a1m+a2q, and Q=b1m+b2q, where a's and b's are some dependent parameters. The condensation of a Van der Waals Boltzmann gas is studied and the variations of the critical pressure Pc and the critical temperature Tc with are analyzed. A study of the phase diagram shows that the isothermals shift downward as decreases from unity. The conditions for the occurrence of successive second-order liquid-gas and solid-liquid transitions are found and it is shown that a tricritical point may exist both in symmetrical and asymmetrical models at the liquid-gas transition depending on the strengths of interactions. Considering the different possible values of m, q, M, and Q four different possible solid phases can be conceived along with two different liquid phases so that the model permits five consequent solid-solid transitions and one liquid-liquid transition. © 1979 The American Physical Society.