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<p>We use effective string theory (EST) to describe a toroidal 2d domain wall embedded in a 3d torus. In particular, we use TBA to compute the free energy of the domain wall in an expansion in inverse powers of the area, up to the second non-universal order that involves the Wilson coefficient <i>γ</i><sub>3</sub>.</p><p>In order to test our predictions, we simulate the 3d Ising model with anti-periodic boundary conditions, using a two-step flat-histogram Monte Carlo method in an ensemble over the boundary coupling <i>J</i> that delivers high-precision free energy data. The predictions from EST reproduce the lattice results with only two adjustable parameters: the string tension, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mn>1</mn> <mo>/</mo> <msubsup> <mi>ℓ</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( 1/{\ell}_s^2 \)</EquationSource> </InlineEquation>, and <i>γ</i><sub>3</sub>. We find <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>γ</mi> <mn>3</mn> </msub> <mo>/</mo> <mfenced close="|" open="|"> <msubsup> <mi>γ</mi> <mn>3</mn> <mi>min</mi> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {\gamma}_3/\left|{\gamma}_3^{\mathrm{min}}\right| \)</EquationSource> </InlineEquation> = −0.82(15), which is compatible with previous estimates.</p>

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Effective string theory on a torus: the 3d Ising domain wall

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  • 发表日期：

    2026年7月29日

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  • David Lima,
  • J. M. Viana Parente Lopes,
  • José Matos,
  • Joao Penedones

摘要

We use effective string theory (EST) to describe a toroidal 2d domain wall embedded in a 3d torus. In particular, we use TBA to compute the free energy of the domain wall in an expansion in inverse powers of the area, up to the second non-universal order that involves the Wilson coefficient γ3.

In order to test our predictions, we simulate the 3d Ising model with anti-periodic boundary conditions, using a two-step flat-histogram Monte Carlo method in an ensemble over the boundary coupling J that delivers high-precision free energy data. The predictions from EST reproduce the lattice results with only two adjustable parameters: the string tension, 1 / ℓ s 2 \( 1/{\ell}_s^2 \) , and γ3. We find γ 3 / γ 3 min \( {\gamma}_3/\left|{\gamma}_3^{\mathrm{min}}\right| \) = −0.82(15), which is compatible with previous estimates.