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arXiv:2511.07207

Dynamical universality class for competing short- and long-range interactions

de Kemmeter, Jean-François, Stefano Ruffo, Gherardini, Stefano

Published Nov 10, 2025• 0 citations
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Abstract

Understanding the dynamical universality classes of systems with long-range interactions remains a key challenge in statistical physics. In this Letter, we analytically and numerically investigate the non-equilibrium critical dynamics of the one-dimensional spin-$1/2$ Nagle-Kardar model, which is characterized by the competition between short- and long-range interactions and the presence of a tricritical point. We focus on the slowing-down of the magnetization $m$ at criticality under Glauber dynamics. Starting from the corresponding master equation, we perform a coarse-graining procedure to obtain a Fokker-Planck equation for the macroscopic variables. Then, the asymptotic decay of the magnetization is derived using central manifold theory. We find that $m$ decays as $t^{-1/2}$ along the critical line and as $t^{-1/4}$ precisely at the tricritical point. This finding confirms that the dynamical critical exponent is $z=2$ as for mean-field models, proving that the macroscopic critical dynamics of the Nagle-Kardar model falls within the dynamical universality class of purely relaxational, non-conserved order parameters (model A). While Kardar proved that the equilibrium Curie-Weiss theory extends to Ising models where nearest-neighbor interactions are included, we here show that such result is valid also for critical dynamics. Our work provides the semi-analytical solution for the critical dynamics of a model with mixed-range interactions, assigning its universality class.

DOI
10.48550/arxiv.2511.07207

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Abstract The equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, with , and we focus on the two-time autocorrelation function . We find that it obeys the scaling form , where is the typical domain size at time t , and where can only be of two types. For , when domain walls diffuse freely, falls in the nearest-neighbour (nn) universality class. Conversely, for , when domain walls dynamics is driven, displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of for , is in the nn universality class ( ) and for .