Relaxation time for competing short- and long-range interactions in the model A dynamic universality class
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arXiv
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| Natura: | Preprint |
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2025
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| author | de Kemmeter, Jean-François Ruffo, Stefano Gherardini, Stefano |
| author_facet | de Kemmeter, Jean-François Ruffo, Stefano Gherardini, Stefano |
| contents | We study the relaxation dynamics at criticality in the one-dimensional spin-$1/2$ Nagle-Kardar model, where short- and long-range interactions can compete. The phase diagram of this model shows lines of first and second-order phase transitions, separated by a tricritical point. We consider Glauber dynamics, focusing on the slowing-down of the magnetization $m$ both along the critical line and at the tricritical point. Starting from the master equation and performing a coarse-graining procedure, we obtain a Fokker-Planck equation for $m$ and the fraction of defects. Using central manifold theory, we analytically show that $m$ decays asymptotically as $t^{-1/2}$ along the critical line, and as $t^{-1/4}$ at the tricritical point. This result implies that the dynamical critical exponent is $z=2$, proving that the macroscopic critical dynamics of the Nagle-Kardar model falls within the dynamic universality class of purely relaxational dynamics with a non-conserved order parameter (model A). Large deviation techniques enable us to show that the average first passage time between local equilibrium states follows an Arrhenius law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relaxation time for competing short- and long-range interactions in the model A dynamic universality class de Kemmeter, Jean-François Ruffo, Stefano Gherardini, Stefano Statistical Mechanics We study the relaxation dynamics at criticality in the one-dimensional spin-$1/2$ Nagle-Kardar model, where short- and long-range interactions can compete. The phase diagram of this model shows lines of first and second-order phase transitions, separated by a tricritical point. We consider Glauber dynamics, focusing on the slowing-down of the magnetization $m$ both along the critical line and at the tricritical point. Starting from the master equation and performing a coarse-graining procedure, we obtain a Fokker-Planck equation for $m$ and the fraction of defects. Using central manifold theory, we analytically show that $m$ decays asymptotically as $t^{-1/2}$ along the critical line, and as $t^{-1/4}$ at the tricritical point. This result implies that the dynamical critical exponent is $z=2$, proving that the macroscopic critical dynamics of the Nagle-Kardar model falls within the dynamic universality class of purely relaxational dynamics with a non-conserved order parameter (model A). Large deviation techniques enable us to show that the average first passage time between local equilibrium states follows an Arrhenius law. |
| title | Relaxation time for competing short- and long-range interactions in the model A dynamic universality class |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2511.07207 |