# Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations

@article{Cirillo2014MetastabilityFG, title={Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations}, author={Emilio N. M. Cirillo and Francesca R. Nardi and Julien Sohier}, journal={Journal of Statistical Physics}, year={2014}, volume={161}, pages={365-403} }

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical…

## 33 Citations

### Effect of Energy Degeneracy on the Transition Time for a Series of Metastable States

- MathematicsJournal of Statistical Physics
- 2021

We consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in…

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- PhysicsEntropy
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Metastability is a ubiquitous phenomenon in nature, which interests several fields of natural sciences. Since metastability is a genuine non-equilibrium phenomenon, its description in the framework…

### Sum of exit times in a series of two metastable states

- Mathematics
- 2017

Abstract
The problem of not degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains is considered. Metastability has been widely…

### Metastability for the Ising model on the hexagonal lattice

- MathematicsElectronic Journal of Probability
- 2022

We consider the Ising model on the hexagonal lattice evolving according to Metropolis dynamics. We study its metastable behavior in the limit of vanishing temperature when the system is immersed in a…

### Approximation method to metastability: an application to non-reversible, two-dimensional Ising and Potts models without external fields

- Mathematics
- 2022

The main contribution of the current study is two-fold. First, we investigate the energy landscape of the Ising and Potts models on finite two-dimensional lattices without external fields in the low…

### Metastability for the degenerate Potts model with negative external magnetic field under Glauber dynamics

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- 2022

We consider the ferromagnetic q-state Potts model on a finite grid with a non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by…

### Metastability of hard-core dynamics on bipartite graphs

- Mathematics
- 2018

We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear…

### Metastability of the three-state Potts model with general interactions

- Mathematics
- 2022

We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants J ij > 0, where i, j ∈ { 1 , 2 , 3 } are the possible spin values (or colors). The…

### Energy Landscape and Metastability of Stochastic Ising and Potts Models on Three-dimensional Lattices Without External Fields

- Physics
- 2021

In this study, we investigate the energy landscape of the Ising and Potts models on fixed and finite but large three-dimensional (3D) lattices where no external field exists and quantitatively…

### Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space…

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