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arXiv · 2606.25919

Macroscopic Fokker-Planck equation from microscopic Glauber dynamics for the Nagle-Kardar model

Jean-François de Kemmeter·Stefano Ruffo·Stefano Gherardini
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Abstract

In the companion Letter we have highlighted the dynamical universality class of the Nagle-Kardar model, where a mean-field interaction is added to the one-dimensional nearest-neighbor Ising model. Starting from the microscopic Glauber dynamics, this paper provides a complete derivation of the Fokker-Planck equation that describes the time evolution of the macroscopic variables (magnetization and defect density) appearing in the model's Hamiltonian. The study of the Langevin equation, associated with the Fokker-Planck equation, allowed us to prove that the model belongs to the universal class of systems with diffusive dynamics and non-conserved order parameter (model A). To this goal, we used several features of the model at equilibrium, including the phase diagram and the fluctuations of macroscopic variables, which are here discussed for completeness. The derivation of the Fokker-Planck equation requires the solution of some combinatorial problems that appear in the counting of configurations at an intermediate level between the microscopic Glauber dynamics and the macroscopic Fokker-Planck one. Finally, we apply both the Glauber and the Langevin dynamics to the study of the average first passage time between local equilibrium states. We confirm that this time obeys an exponential Arrhenius law in terms of system's size, offering a direct link between microscopic energy landscapes and macroscopic relaxation mechanisms.

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Jean-François de Kemmeter, Stefano Ruffo, Stefano Gherardini. 2026-06-24. Macroscopic Fokker-Planck equation from microscopic Glauber dynamics for the Nagle-Kardar model. https://arxiv.org/abs/2606.25919

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