Rigorous lower bound of the dynamical critical exponent of the Ising model

TL;DR

This paper rigorously establishes a lower bound on the dynamical critical exponent of the Ising model, improving previous estimates by connecting stochastic dynamics to quantum systems and applying key inequalities.

Contribution

It introduces a novel proof technique linking stochastic processes to quantum systems to derive bounds on critical exponents.

Findings

Proves the lower bound z ≥ 2 for the Ising model's dynamical critical exponent.

Improves upon the previous estimate z ≥ 2 - η.

Utilizes inequalities from quantum many-body physics to establish the bound.

Abstract

We study the kinetic Ising model under Glauber dynamics and establish an upper bound on the spectral gap for finite systems. This bound implies the critical exponent inequality $z \geq 2$, thereby rigorously improving the previously known estimate $z \geq 2 - \eta$. Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon--Lieb and Gosset--Huang inequalities.