Quench below the critical temperature in the Ising model: asymptotic state versus equilibrium under various boundary conditions

Abstract

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.