# Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model

Source: [Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model](<https://www.sota2.com/research/paper/68fa28692c2a3760193c81d4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:52.807Z

Authors: F.Corberi, E.Lippiello, M.Zannetti

Published: 2008-07-02T17:17:45.000Z

## Abstract

We study the role of the quench temperature $T\_f$ in the phase-ordering kinetics of the Ising model with single spin flip in $d=2,3$. Equilibrium interfaces are flat at $T\_f=0$, whereas at $T\_f\>0$ they are curved and rough (above the roughening temperature in $d=3$). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent $z=2$ of the size of domains $L(t)\\sim t^{1/z}$ is unaffected by $T\_f$, other exponents related to the interface geometry take different values at $T\_f=0$ or $T\_f\>0$. For $T\_f\>0$ a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at $T\_f=0$, to the asymptotic regime with curved interfaces characteristic of $T\_f\>0$. Furthermore, it is shown that the roughening length, although sub-dominant with respect to $L(t)$, produces appreciable correction to scaling up to very long times in $d=2$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0807.0402>)

[PDF](<https://arxiv.org/pdf/0807.0402.pdf>)