Non-reciprocal interactions preserve the universality class of Potts model
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arXiv
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| Format: | Preprint |
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2024
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| author | Saha, Soumya K. Mohanty, P. K. |
| author_facet | Saha, Soumya K. Mohanty, P. K. |
| contents | 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 $ξ_2/ξ_0$, where $ξ_2$ is the second moment correlation length and $ξ_0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-reciprocal interactions preserve the universality class of Potts model Saha, Soumya K. Mohanty, P. K. Statistical Mechanics Soft Condensed Matter Cellular Automata and Lattice Gases 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 $ξ_2/ξ_0$, where $ξ_2$ is the second moment correlation length and $ξ_0$ 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. |
| title | Non-reciprocal interactions preserve the universality class of Potts model |
| topic | Statistical Mechanics Soft Condensed Matter Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2412.19664 |