Dynamics and thermodynamics of rotators interacting with both long and short range couplings

TL;DR

This paper investigates how adding nearest-neighbor interactions affects the thermodynamics and dynamics of the Hamiltonian Mean Field model, revealing phase transitions, ensemble inequivalence, and metastable state behaviors.

Contribution

It introduces the study of combined long-range and short-range couplings in the HMF model, highlighting new phase transition phenomena and metastability characteristics.

Findings

First order phase transition observed with antiferromagnetic nearest-neighbor coupling.

Canonical and microcanonical ensembles are non-equivalent in this model.

Metastable states have lifetimes increasing exponentially with system size.

Abstract

The effect of nearest-neighbor coupling on the thermodynamic and dynamical properties of the ferromagnetic Hamiltonian Mean Field model (HMF) is studied. For a range of antiferromagnetic nearest-neighbor coupling, a canonical first order transition is observed, and the canonical and microcanonical ensembles are non-equivalent. In studying the relaxation time of non-equilibrium states it is found that as in the HMF model, a class of non-magnetic states is quasi-stationary, with an algebraic divergence of their lifetime with the number of degrees of freedom $N$. The lifetime of metastable states is found to increase exponentially with $N$ as expected.