Domain growth in long-range Ising models with disorder

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 $$J(r) \sim r^{-(D+\sigma )}$$ J ( r ) ∼ r - ( D + σ ) , where D is the spatial dimension and $$\sigma > 0$$ 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: $$R(t) \sim (\ln t)^{\alpha }$$ R ( t ) ∼ ( ln t ) α , with growth exponent $$\alpha >0$$ α > 0 . Here, we examine how long-range interactions influence domain growth with disorder in dimensions $$D = 1$$ D = 1 and $$D = 2$$ D = 2 . In $$D = 1$$ D = 1 , logarithmic growth is found to persist for various $$\sigma > 0$$ σ > 0 . However, in $$D = 2$$ D = 2 , the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations. Graphic Abstract