Monte Carlo study of entropy for face-centered cubic Ising antiferromagnets

A face-centered cubic Ising model with nearest neighbor antiferromagnetic exchangeJ _nn in the presence of a magnetic fieldH is investigated by Monte Carlo methods. Free energy and entropy of the model are obtained by integrating the equation of state along various paths, starting at suitable reference states. It is shown that at low temperatures first-order phase transitions can be located with very good precision. At the two critical fieldsH _c1/|J _nn |=4,H _c2/|J _nn |=12 a residual ground-state entropyS(0) is found, which is estimated as aboutS(0)/k _B (ln 2)/3 in both cases.In the presence of a ferromagnetic next-nearest neighbor exchange there is no longer a nonzero entropy at the critical fields, however. ForR+J _nnn /J _nn +–1 we find the same structure of the phase diagram as qualitatively predicted by Domany et al., where lines of 3-state and 4-state Potts model-like transitions meet at a multicritical point atH=0. Some consequences of our results for interpreting the ordering of face-centered cubic binary alloys are also discussed.