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

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.

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• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point
• Gravothermal instability with a cosmological constant in the canonical ensemble
• Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions
• Canonical equilibrium of mean-field $O(n)$~models in the presence of random fields
• Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction
• Non-mean-field effects in systems with long-range forces in competition