Out-of-equilibrium percolation transitions at finite critical times after quenches across magnetic first-order transitions
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arXiv
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| Natura: | Preprint |
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2026
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| author | Pelissetto, Andrea Rossini, Davide Vicari, Ettore |
| author_facet | Pelissetto, Andrea Rossini, Davide Vicari, Ettore |
| contents | We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature first-order transition line by a quench of the magnetic field $h$ from $h_i<0$ to $h>0$. In the thermodynamic limit and for finite values of $h$, the post-quench evolution under a purely relaxational dynamics is characterized by a dynamic transition at a finite critical time $t_c(h)$ from the metastable negatively magnetized phase to the positive one, marked by the percolation of the largest clusters of positive and negative spins. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on $h$. We also show that the percolation critical behavior is related to the spinodal-like behavior of the magnetization in the small-$h$ limit, which implies that the percolation time $t_c(h)$ exhibits a spinodal-like exponential dependence on $h$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13127 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Out-of-equilibrium percolation transitions at finite critical times after quenches across magnetic first-order transitions Pelissetto, Andrea Rossini, Davide Vicari, Ettore Statistical Mechanics High Energy Physics - Lattice We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature first-order transition line by a quench of the magnetic field $h$ from $h_i<0$ to $h>0$. In the thermodynamic limit and for finite values of $h$, the post-quench evolution under a purely relaxational dynamics is characterized by a dynamic transition at a finite critical time $t_c(h)$ from the metastable negatively magnetized phase to the positive one, marked by the percolation of the largest clusters of positive and negative spins. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on $h$. We also show that the percolation critical behavior is related to the spinodal-like behavior of the magnetization in the small-$h$ limit, which implies that the percolation time $t_c(h)$ exhibits a spinodal-like exponential dependence on $h$. |
| title | Out-of-equilibrium percolation transitions at finite critical times after quenches across magnetic first-order transitions |
| topic | Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2603.13127 |