Phase transitions in simplified models with long-range interactions

TL;DR

This paper investigates phase transitions in simplified long-range interaction models, showing that certain predicted transitions do not occur and identifying the main entropy maximization mechanism behind observed phase behaviors.

Contribution

It introduces a new class of solvable models without critical points, clarifies the nature of phase transitions, and refutes a recent prediction of a phase transition in the ring model.

Findings

No phase transition in the ring model as previously predicted.

Identification of a first order phase transition from homogeneous to clustered states.

Observation of a core-halo to core configuration change at low energies.

Abstract

We study the origin of phase transitions in some simplified models with long range interactions. For the ring model, we show that a possible new phase transition predicted in a recent paper by Nardini and Casetti from an energy landscape analysis does not occur. Instead of such phase transitions we observe a sharp, although without any non-analiticity, change from a core-halo to an only core configuration in the spatial distribution functions for low energies. By introducing a new class of solvable simplified models without any critical points in the potential energy, we show that a similar behaviour to the ring model is obtained, with a first order phase transition from an almost homogeneous high energy phase to a clustered phase, and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features of the simplified models, and show that the first order phase transition comes from the maximization of the entropy of the system as a function of energy an an order parameter, as previously discussed by Kastner, which seems to be the main mechanism causing phase transitions in long-range interacting systems.