Short-time dynamics in the 2D Blume-Capel model, with a non-conserved order-parameter and short-ranged interactions, is analysed. For non-equilibrium dynamics, both at a critical point in the 2D Ising universality class and at the tricritical point, we reproduce the values <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Theta =0.190({5})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mo>=</mo> <mn>0.190</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Theta =-0.542({5})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mo>=</mo> <mo>-</mo> <mn>0.542</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, respectively, of the critical initial slip exponent. These agree with more early estimates and with the Janssen-Schaub-Schmittmann scaling relation. In phase-ordering kinetics, after a quench into the ordered phase, we establish the validity of short-time dynamics. In the 2D Ising universality class, we find <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\Theta =0.39({1})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Θ</mi> <mo>=</mo> <mn>0.39</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in agreement with the scaling relation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\lambda =d-2\Theta $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mi>d</mi> <mo>-</mo> <mn>2</mn> <mi mathvariant="normal">Θ</mi> </mrow> </math></EquationSource> </InlineEquation>.

Short-Time Dynamics in Phase-Ordering Kinetics

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发表日期：

2026年3月12日

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Leïla Moueddene,
Malte Henkel

摘要

Short-time dynamics in the 2D Blume-Capel model, with a non-conserved order-parameter and short-ranged interactions, is analysed. For non-equilibrium dynamics, both at a critical point in the 2D Ising universality class and at the tricritical point, we reproduce the values $\Theta =0.190({5})$ $Θ = 0.190 (5)$ and $\Theta =-0.542({5})$ $Θ = - 0.542 (5)$ , respectively, of the critical initial slip exponent. These agree with more early estimates and with the Janssen-Schaub-Schmittmann scaling relation. In phase-ordering kinetics, after a quench into the ordered phase, we establish the validity of short-time dynamics. In the 2D Ising universality class, we find $\Theta =0.39({1})$ $Θ = 0.39 (1)$ in agreement with the scaling relation $\lambda =d-2\Theta $ $λ = d - 2 Θ$ .