# 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

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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…

### Metastability of Synchronous and Asynchronous Dynamics

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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

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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
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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…

### Critical Configurations and Tube of Typical Trajectories for the Potts and Ising Models with Zero External Field

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We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature…

### 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…

### Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions

- Mathematics
- 2017

We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of…

### Tunneling behavior of Ising and Potts models in the low-temperature regime

- PhysicsStochastic Processes and their Applications
- 2019

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