# Metastability for the Ising model on the hexagonal lattice

@article{Apollonio2021MetastabilityFT, title={Metastability for the Ising model on the hexagonal lattice}, author={Valentina Apollonio and Vanessa Jacquier and Francesca R. Nardi and Alessio Troiani}, journal={Electronic Journal of Probability}, year={2021} }

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 small external magnetic field. We determine the asymptotic properties of the transition time from the metastable to the stable state up to a multiplicative factor and study the mixing time and the spectral gap of the Markov process. We give a geometrical description of the critical configurations…

## 8 Citations

### Metastability for Kawasaki Dynamics on the Hexagonal Lattice

- MathematicsJournal of Statistical Physics
- 2023

In this paper we analyze the metastable behavior for the Ising model that evolves under Kawasaki dynamics on the hexagonal lattice $${\mathbb {H}}^2$$ H 2 in the limit of vanishing temperature. Let…

### 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…

### Metastability of Ising and Potts Models Without External Fields in Large Volumes at Low Temperatures

- MathematicsCommunications in Mathematical Physics
- 2022

In this article, we investigate the energy landscape and metastable behavior of Ising and Potts models on two-dimensional square or hexagonal lattices in the low-temperature regime, especially in the…

### Critical Droplets and Sharp Asymptotics for Kawasaki Dynamics with Strongly Anisotropic Interactions

- PhysicsJournal of Statistical Physics
- 2022

In this paper we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Let Λ⊂Z2\documentclass[12pt]{minimal}…

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

- MathematicsJournal of Mathematical Physics
- 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…

### Shaken Dynamics: An Easy Way to Parallel Markov Chain Monte Carlo

- Materials ScienceJournal of Statistical Physics
- 2022

We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function H(σ)\documentclass[12pt]{minimal}…

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

- MathematicsJournal of Statistical Physics
- 2021

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…

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