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

Abstract

We consider the relaxation time for the Glauber dynamics of infinite-volume critical ferromagnetic Ising model on ${\mathbb{Z}}^d$ in any dimension $d\ge 2$. 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.

Generalized the main result to all dimensions; Final version