Polynomial rate of relaxation for the Glauber dynamics of infinite-volume critical Ising model

TL;DR

This paper proves that the spin correlation function in the infinite-volume critical Ising model decays polynomially over time, under certain assumptions, revealing insights into the dynamics at criticality.

Contribution

It establishes a polynomial decay rate for the relaxation time of the Glauber dynamics at criticality, based on finite-volume log-Sobolev and arm exponent assumptions.

Findings

Polynomial decay of spin correlations over time

Dependence on finite-volume log-Sobolev constant and arm exponent

Insights into critical dynamics of the Ising model

Abstract

We consider the relaxation time for the Glauber dynamics of infinite-volume critical ferromagnetic Ising model on $\Z^{d}$ in any dimension $d\geq2$. Under the assumptions regarding the finite-volume log-Sobolev constant and the 1-arm exponent of the critical 1-spin expectation, we show that the equal-position temporal spin correlation function decays polynomially fast in time.