# Non-reciprocal interactions preserve the universality class of Potts model

Source: [Non-reciprocal interactions preserve the universality class of Potts model](<https://www.sota2.com/research/paper/68fa48ec1e209131ce9334c1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T07:05:32.186Z

Authors: Soumya K. Saha, P. K. Mohanty

Published: 2024-12-27T14:22:56.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2412.19664>)

[PDF](<https://arxiv.org/pdf/2412.19664.pdf>)