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… 
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7 Citations
Background Citations
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Methods Citations
5

7 Citations

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References

SHOWING 1-10 OF 64 REFERENCES

Polyiamonds and Polyhexes with Minimum Site-Perimeter and Achievement Games

The site-perimeter of an animal is the number of empty cells connected to the animal by an edge, and the minimum site- perimeter with a given cell size is found for animals on the triangular and hexagonal grid.

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

We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an…

Shaken dynamics for 2d ising models.

We define a Markovian parallel dynamics for a class of nearest neighbor spin systems. In the dynamics, beside the two usual parameters $J$, the strength of the interaction, and $\lambda$, the…

On the metastability in three modifications of the Ising model

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model (see Chapter 2) is an anisotropic version, where the…

Criticality of Measures on 2-d Ising Configurations: From Square to Hexagonal Graphs

On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter…

Low temperature stochastic dynamics for an Ising model with alternating field

On the Essential Features of Metastability: Tunnelling Time and Critical Configurations

AbstractWe consider Metropolis Markov chains with finite state space and transition probabilities of the form $$P(\eta ,\eta ')=q(\eta ,\eta ')e^{- \beta [H(\eta ') - H(\eta)]_+}$$ for given energy…

Critical droplets and metastability for a Glauber dynamics at very low temperatures

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the…

Metropolis Dynamics Relaxation via Nucleation and Growth

Abstract:We consider the Ising model with Metropolis dynamics on under a small positive external field h. We show that the relaxation time, i.e., the time it takes for the system to reach the…

Behavior of droplets for a class of Glauber dynamics at very low temperature

SummaryWe consider a class of Glauber dynamics for the two-dimensional nearest neighbor ferromagnetic Ising model in which the rate with which each spin flips depends only on the increment in energy…
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