Out-of-equilibrium finite-time percolation transitions and spinodal-like behaviors after quenches across magnetic first-order transitions of Ising systems
Abstract
We analyze the out-of-equilibrium relaxational dynamics of ferromagnetic Ising-like systems driven across their low-temperature magnetic first-order transition (FOT) line, by sudden and slow variations of an external homogenous magnetic field h. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature FOT line by suddently quenching h from hi<0 to h>0, inducing a transition from the negatively to the positively magnetized phase. We show the emergence of a dynamic percolation transition at a finite critical time tc(h) along the post-quench evolution for finite (sufficiently small) values of h, which is marked by the percolation of the largest positive-spin cluster and the antipercolation of the largest negative-spin cluster. 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 transition marks the passage from the metastable negatively-magnetized phase to the stable positively-magnetized one. Therefore, in the small-h limit, the percolation critical behavior is related to the spinodal-like behavior of the magnetization, implying that the percolation time tc(h) exhibits a spinodal-like exponential dependence on h. The existence of percolation transitions is likely a generic phenomenon at magnetic Ising-like FOTs. For example, we observe an analogous behavior in dynamic (Kibble-Zurek-like) protocols entailing slow variations of the magnetic field driving the crossing of the FOT line.
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BibTeX
@misc{pelissetto2026outofequilibrium,
title = {{Out-of-equilibrium finite-time percolation transitions and spinodal-like behaviors after quenches across magnetic first-order transitions of Ising systems}},
author = {Andrea Pelissetto and Davide Rossini and Ettore Vicari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35485},
eprint = {2609.35485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35485},
}
RIS
TY - UNPB
TI - Out-of-equilibrium finite-time percolation transitions and spinodal-like behaviors after quenches across magnetic first-order transitions of Ising systems
AU - Andrea Pelissetto
AU - Davide Rossini
AU - Ettore Vicari
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35485
UR - https://arxiv.org/abs/2609.35485
AB - We analyze the out-of-equilibrium relaxational dynamics of ferromagnetic Ising-like systems driven across their low-temperature magnetic first-order transition (FOT) line, by sudden and slow variations of an external homogenous magnetic field h. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature FOT line by suddently quenching h from h_i<0 to h>0, inducing a transition from the negatively to the positively magnetized phase. We show the emergence of a dynamic percolation transition at a finite critical time t_c(h) along the post-quench evolution for finite (sufficiently small) values of h, which is marked by the percolation of the largest positive-spin cluster and the antipercolation of the largest negative-spin cluster. 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 transition marks the passage from the metastable negatively-magnetized phase to the stable positively-magnetized one. Therefore, in the small-h limit, the percolation critical behavior is related to the spinodal-like behavior of the magnetization, implying that the percolation time t_c(h) exhibits a spinodal-like exponential dependence on h. The existence of percolation transitions is likely a generic phenomenon at magnetic Ising-like FOTs. For example, we observe an analogous behavior in dynamic (Kibble-Zurek-like) protocols entailing slow variations of the magnetic field driving the crossing of the FOT line.
ER -