Non-equilibrium scaling across first-order transitions with relativistic scalar fields
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| Format: | Preprint |
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2026
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| _version_ | 1866910208205258752 |
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| author | Sieke, Leon J. Fuchs, Jessica von Smekal, Lorenz |
| author_facet | Sieke, Leon J. Fuchs, Jessica von Smekal, Lorenz |
| contents | We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-equilibrium scaling across first-order transitions with relativistic scalar fields Sieke, Leon J. Fuchs, Jessica von Smekal, Lorenz High Energy Physics - Phenomenology Statistical Mechanics We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter. |
| title | Non-equilibrium scaling across first-order transitions with relativistic scalar fields |
| topic | High Energy Physics - Phenomenology Statistical Mechanics |
| url | https://arxiv.org/abs/2605.10346 |