Eur. Phys. J. B (2025) 98: 187
https://doi.org/10.1140/epjb/s10051-025-01035-9

Research - Statistical and Nonlinear Physics

Domain growth in long-range Ising models with disorder

¹ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy
² Dipartimento di Fisica “E. R. Caianiello”, and INFN, Gruppo Collegato di Salerno, and CNISM, Università di Salerno, via Giovanni Paolo II 132, 84084, Fisciano (SA), Italy
³ Dipartimento di Matematica e Fisica, Università della Campania, Viale Lincoln 5, 81100, Caserta, Italy
⁴ School of Physical Sciences, Jawaharlal Nehru University, New Mehrauli Road, 110067, New Delhi, India

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Received: 3 July 2025
Accepted: 29 August 2025
Published online: 13 September 2025

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: $R(t)\sim {(lnt)}^{\alpha }$, 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.