Domain Growth in Long-range Ising Models with Disorder

TL;DR

This paper studies how domain growth behaves in long-range disordered Ising models at low temperatures, revealing persistent logarithmic growth in one dimension and complex dynamics in two dimensions due to the interplay of interactions and disorder.

Contribution

It investigates the effects of long-range interactions and quenched disorder on domain growth in Ising models across different dimensions, highlighting dimension-dependent behaviors.

Findings

Logarithmic domain growth persists in 1D for various interaction ranges.

In 2D, domain growth exhibits complex, non-trivial dynamics.

Disorder influences the interplay between long-range interactions and thermal fluctuations.

Abstract

Recent advances have highlighted the rich low-temperature kinetics of the long-range Ising model (LRIM). This study investigates domain growth in an LRIM with quenched disorder, following a deep low-temperature quench. Specifically, we consider an Ising model with interactions that decay as $J(r) \sim r^{-(D+\sigma)}$, where $D$ is the spatial dimension and $\sigma > 0$ is the power-law exponent. The quenched disorder is introduced via random pinning fields at each lattice site. For nearest-neighbor models, we expect that domain growth during activated dynamics is logarithmic in nature: $R(t) \sim (\ln t)^{\alpha}$, with growth exponent $\alpha >0$. Here, we examine how long-range interactions influence domain growth with disorder in dimensions $D = 1$ and $D = 2$. In $D = 1$, logarithmic growth is found to persist for various $\sigma > 0$. However, in $D = 2$, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations.