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.

5+6 pages, v2: published version

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• Criticality, the area law, and the computational power of PEPS
• Dynamics at and near conformal quantum critical points
• The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion
• Quantitatively improved finite-size criteria for spectral gaps
• Quadratic dispersion relations in gapless frustration-free systems
• On the critical finite-size gap scaling for frustration-free Hamiltonians

Cited by in corpus (2)

• Harnessing finite-size effects to gauge aging in the $2D$ Ising model
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain