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

TL;DR

This paper investigates the low-temperature domain growth kinetics of a 2D long-range Ising model, revealing a universal growth exponent of 4/3 at zero temperature due to long-range interactions, supported by simulations and analytical models.

Contribution

It demonstrates that at zero temperature, the domain growth exponent is universally 4/3, independent of the long-range interaction parameter, contrasting with finite temperature predictions.

Findings

At T=0, the growth exponent z=4/3 is universal.

Long-range interactions induce interface drift affecting dynamics.

Monte Carlo simulations support the analytical findings.

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.