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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3456_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(z \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, thereby rigorously improving the previously known estimate <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3456_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(z \ge 2 - \eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>≥</mo> <mn>2</mn> <mo>-</mo> <mi>η</mi> </mrow> </math></EquationSource> </InlineEquation>. Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon–Lieb and Gosset–Huang inequalities.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月26日

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  • Rintaro Masaoka,
  • Tomohiro Soejima,
  • Haruki Watanabe

摘要

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 \(z \ge 2\) z ≥ 2 , thereby rigorously improving the previously known estimate \(z \ge 2 - \eta \) 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.