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<p>Exact single-time and two-time correlations and the two-time response function are found for the order-parameter in the voter model with nearest-neighbour interactions. Their explicit dynamical scaling functions are shown to be continuous functions of the space dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. Their form reproduces the predictions of non-equilibrium representations of the Schrödinger algebra for models with dynamical exponent <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/10773_2025_6151_IEq2_HTML.png" Format="PNG" Height="12" Rendition="HTML" Resolution="120" Type="Linedraw" Width="38" /> </InlineMediaObject> </InlineEquation> and with the dominant noise-source coming from the heat bath. Hence the ageing in the voter model is a paradigm for relaxations in non-equilibrium critical dynamics, without detailed balance, and with the upper critical dimension <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(d^*=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>d</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Schrödinger-invariance in the Voter Model

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Malte Henkel,
  • Stoimen Stoimenov

摘要

Exact single-time and two-time correlations and the two-time response function are found for the order-parameter in the voter model with nearest-neighbour interactions. Their explicit dynamical scaling functions are shown to be continuous functions of the space dimension \(d>0\) d > 0 . Their form reproduces the predictions of non-equilibrium representations of the Schrödinger algebra for models with dynamical exponent and with the dominant noise-source coming from the heat bath. Hence the ageing in the voter model is a paradigm for relaxations in non-equilibrium critical dynamics, without detailed balance, and with the upper critical dimension \(d^*=2\) d ∗ = 2 .