Non-reciprocal interactions preserve the universality class of Potts model

TL;DR

This study investigates how non-reciprocal interactions in the Potts model affect critical behavior, finding that while some critical exponents change, the overall universality class remains consistent with equilibrium models, revealing superuniversality features.

Contribution

The paper demonstrates that non-reciprocal interactions do not alter the universality class of the Potts model and uncovers super-universal scaling functions in non-equilibrium settings.

Findings

Critical exponents for q=2 match equilibrium Ising class.

Critical exponents for q=3,4 vary continuously.

Super-universal Binder cumulant scaling function is preserved.

Abstract

We study the $q$-state Potts model on a square lattice with directed nearest-neighbor spin-spin interactions that are inherently non-reciprocal. Both equilibrium and non-equilibrium dynamics are investigated. Analytically, we demonstrate that non-reciprocal interactions do not alter the critical exponents of the model under equilibrium dynamics. In contrast, numerical simulations with selfish non-equilibrium dynamics reveal distinctive behavior. For $q=2$ (non-reciprocal non-equilibrium Ising model), the critical exponents remain consistent with those of the equilibrium Ising universality class. However, for $q=3$ and $q=4$, the critical exponents vary continuously. Remarkably, a super-universal scaling function -- Binder cumulant as a function of $\xi_2/\xi_0$, where $\xi_2$ is the second moment correlation length and $\xi_0$ its maximum value -- remains identical to that of the equilibrium $q=3,4$ Potts models. These findings indicate that non-reciprocal Potts models belong to the superuniversality class of their respective equilibrium counterparts.