Restriction and mixing properties of interacting particle systems with unbounded range

TL;DR

This paper establishes explicit error bounds and decay of correlations for interacting particle systems with unbounded range, demonstrating that exponential decay of interactions prevents spontaneous symmetry breaking.

Contribution

It provides non-asymptotic bounds for approximating infinite-volume dynamics and shows that exponential decay of interactions inhibits symmetry breaking in such systems.

Findings

Explicit non-asymptotic error bounds for finite approximations

Quantitative bounds on spatial decay of correlations

Exponential decay interactions prevent spontaneous symmetry breaking

Abstract

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many interacting particles. Moreover, we also provide non-asymptotic quantitative bounds on the spatial decay of correlations at times $t>0$ and then apply these results to show that interacting particle systems on $\mathbb{Z}$ whose interaction strengths decays exponentially fast cannot spontaneously break the time-translation symmetry, neither in the strong, nor in the weak sense.