We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling J(r)∼r-(d+σ), where d=2 is the dimensionality. According to the Bray-Rutenberg predictions, the exponent σ controls the algebraic growth in time of the characteristic domain size L(t), L(t)∼t1/z, with growth exponent z=1+σ for σ<1 and z=2 for σ>1. These results hold for quenches to a nonzero temperature T>0 below the critical temperature Tc. 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, independently of σ, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.

Kinetics of the two-dimensional long-range Ising model at low temperatures

Lippiello E.;
2021

Abstract

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling J(r)∼r-(d+σ), where d=2 is the dimensionality. According to the Bray-Rutenberg predictions, the exponent σ controls the algebraic growth in time of the characteristic domain size L(t), L(t)∼t1/z, with growth exponent z=1+σ for σ<1 and z=2 for σ>1. These results hold for quenches to a nonzero temperature T>0 below the critical temperature Tc. 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, independently of σ, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/467186
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