https://doi.org/10.1140/epjb/s10051-025-01082-2
Research - Statistical and Nonlinear Physics
Quench below the critical temperature in the Ising model: asymptotic state versus equilibrium under various boundary conditions
1
CNR-SPIN, c/o Complesso di Monte S. Angelo, via Cinthia, 80126, Naples, Italy
2
Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli “Federico II”, Complesso di Monte S. Angelo, via Cinthia, 80126, Naples, Italy
3
Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, Via Giovanni Paolo II 132, 84084, Fisciano, SA, Italy
Received:
30
May
2025
Accepted:
27
October
2025
Published online:
5
November
2025
The nature of the asymptotic state toward which the system evolves after a quench to below the critical temperature has been recently addressed in the Ising model through exact results, scaling arguments, and numerical simulations. It has been suggested that this state is critical. While this may seem trivial, given that domain coarsening fundamentally involves the unbounded growth of a time-dependent correlation length, which roughly matches the average domain size, the situation is more complex. This complexity arises from the presence of a critical state below the critical temperature, which sharply contradicts the usual Ising equilibrium picture, characterised by symmetry breaking, ferromagnetic order, and short-range correlations. We aim to clarify this issue by analysing the subtle yet crucial role of boundary conditions.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
