Dynamic scaling behavior in the presence of a periodic magnetic driving across Ising continuous transitions

2026/08/06 by Andrea Pelissetto, Ettore Vicari
Physics and Astronomy · #cond-mat.stat-mech #hep-lat

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13 pages

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

We study the critical dynamics arising from a time-dependent periodic homogenous source coupled to the order-parameter field, which drives a classical ferromagnetic system across a continuous transition. For this purpose, we consider the paradigmatic two-dimensional (2D) Ising model in the presence of a periodic magnetic field h(t)=-A cos (2πt/P), evolving under a purely relaxational dynamics at the critical temperature. We show that the periodic driving gives rise to a peculiar dynamic scaling behavior in the thermodynamic limit, arising from a nontrivial interplay among the time t, the amplitude A and period P of h(t). The relevant scaling variables are τ=t/P and σ=A P^κ, with κ= y_h/z, where y_h=(d+2-η)/2 is the critical dimension of the magnetic field, and z is dynamic exponent for the critical relaxational dynamics (κ≈ 0.865 for the 2D Ising model). The dynamic scaling behaviors of the magnetization and bond-energy density show an oscillatory behavior around a smooth curve which approaches a large-τ stationary behavior. We also briefly discuss the dynamic behavior of an Ising system driven across the critical point by a periodic time-varying temperature at zero magnetic field.

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