Domain growth in long-range Ising models with disorder

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)∼r-(D+σ), where D is the spatial dimension and σ>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)∼(lnt)α, with growth exponent α>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 σ>0. However, in D=2, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations.