Long-time asymptotics of the long-range Emch-Radin model

TL;DR

This paper investigates the long-time behavior of a long-range spin model, showing that the relaxation time diverges with system size, leading to quasistationary states and non-observable equilibration in large systems.

Contribution

It analytically establishes bounds on observable expectations and demonstrates divergence of relaxation time with system size in a long-range spin model.

Findings

Relaxation time diverges as system size increases.

System exhibits quasistationary nonequilibrium states.

Equilibration becomes unobservable in large finite systems.

Abstract

The long-time asymptotic behavior is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behavior. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.