Non-equilibrium structures and slow dynamics in a two dimensional spin system with competitive long range and short range interactions

TL;DR

This paper introduces a 2D lattice spin model with competing long-range attraction and short-range repulsion, revealing non-equilibrium disordered structures and slow dynamics after a quench, despite no quenched disorder.

Contribution

The study provides a detailed phase diagram and analyzes non-equilibrium behavior, highlighting slow relaxation and structure formation due to interaction competition.

Findings

Equilibrium phases are ferromagnetic and antiferromagnetic.

Post-quench dynamics show slow relaxation and disordered structures.

Competition between interactions induces slow dynamics without disorder.

Abstract

We introduce a lattice spin model that mimics a system of interacting particle through a short range repulsive potential and a long range attractive power law decaying potential. We performed a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium pases are the ferromagnetic and the antiferromagnetic ones. We then studied the non equilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We found that, even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to non--equilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system.