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

Rintaro Masaoka; Tomohiro Soejima; Haruki Watanabe

doi:10.1007/s10955-025-03456-3

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arXiv · 2502.09908

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

Rintaro Masaoka·Tomohiro Soejima·Haruki Watanabe

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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.

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Rintaro Masaoka, Tomohiro Soejima, Haruki Watanabe. 2025-02-14. Rigorous lower bound of the dynamical critical exponent of the Ising model. https://doi.org/10.1007/s10955-025-03456-3

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