Breaking of ergodicity and long relaxation times in systems with long-range interactions

TL;DR

This paper investigates how long-range interactions in an Ising model lead to ergodicity breaking and diverging relaxation times, revealing fundamental differences from short-range systems in thermodynamic and dynamical behavior.

Contribution

It demonstrates that long-range interactions cause divergence in relaxation times and ergodicity breaking, extending understanding of non-equilibrium dynamics in such systems.

Findings

Relaxation time diverges logarithmically with system size.

Gaps in magnetization can form, preventing state transitions.

Ergodicity breaks down even in finite systems with long-range interactions.

Abstract

The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long range interactions and are expected to be valid even when the interaction is slowly decaying with distance.