# Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures

Source: [Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures](<https://www.sota2.com/research/paper/68fa3ddf1e209131ce8e3c0a>)

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

Data updated: 2025-10-28T13:54:21.939Z

Authors: Ramgopal Agrawal, Federico Corberi, Eugenio Lippiello, Paolo Politi, Sanjay Puri

Published: 2020-11-10T10:45:01.000Z

## Abstract

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \\sim r^{-(d+\\sigma)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $\\sigma$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \\sim t^{1/z}$, with growth exponent $z=1+\\sigma$ for $\\sigma \<1$ and $z=2$ for $\\sigma \>1$. These results hold for quenches to a non-zero temperature $T\>0$ below the critical temperature $T\_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $\\sigma$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2011.05030>)

[PDF](<https://arxiv.org/pdf/2011.05030.pdf>)