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

2025/02/14 by Masaoka, Rintaro, Soejima, Tomohiro, Watanabe, Haruki · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2502.09908

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

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