Models with short- and long-range interactions: the phase diagram and the reentrantphase

Abstract

We study the phase diagram of two different Hamiltonians with competing local,nearest-neighbour, and mean-field couplings. The first example corresponds to the HMFHamiltonian with an additional short-range interaction. The second example is a reducedHamiltonian for dipolar layered spin structures, with a new feature with respect to the firstexample: the presence of anisotropies.The two examples are solved in both the canonical and the microcanonical ensemble usinga combination of the min–max method with the transfer operator method. The phasediagrams present typical features of systems with long-range interactions: ensembleinequivalence, negative specific heat and temperature jumps.Moreover, for a given range of parameters, we report the signature of phase reentrance.This can also be interpreted as the presence of azeotropy with the creation of twofirst-order phase transitions with ensemble inequivalence, as one parameter is variedcontinuously.