Models with short and long-range interactions: phase diagram and reentrant phase

TL;DR

This paper investigates the phase diagrams of two Hamiltonians with competing local, short-range, and mean-field interactions, revealing phenomena like ensemble inequivalence, negative specific heat, and phase reentrance.

Contribution

It introduces a detailed analysis of phase diagrams for Hamiltonians with competing interactions, highlighting reentrant phases and ensemble inequivalence.

Findings

Identification of phase reentrance in the models

Observation of ensemble inequivalence and negative specific heat

Detection of temperature jumps and first-order phase transitions

Abstract

We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second example is a reduced Hamiltonian for dipolar layered spin structures, with a new feature with respect to the first example, the presence of anisotropies. The two examples are solved in both the canonical and the microcanonical ensemble using a combination of the min-max method with the transfer operator method. The phase diagrams present typical features of systems with long-range interactions: ensemble inequivalence, negative specific heat and temperature jumps. Moreover, in 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 two first order phase transitions with ensemble inequivalence, as one parameter is varied continuously.