Rigorous Lower Bound of the Dynamical Critical Exponent of the Ising Model

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 \(z \ge 2\), thereby rigorously improving the previously known estimate \(z \ge 2 - \eta \). Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon–Lieb and Gosset–Huang inequalities.