Corpus ID: 235490688

Low-temperature Ising dynamics with random initializations

@inproceedings{Gheissari2021LowtemperatureID,
  title={Low-temperature Ising dynamics with random initializations},
  author={R. Gheissari and A. Sinclair},
  year={2021}
}
It is well known that Glauber dynamics on spin systems typically suffer exponential slowdowns at low temperatures. This is due to the emergence of multiple metastable phases in the state space, separated by narrow bottlenecks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be polynomially fast. However, such phenomena… Expand

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References

SHOWING 1-10 OF 54 REFERENCES
Critical Ising on the Square Lattice Mixes in Polynomial Time
The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced inExpand
Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree
Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup Pt. A fundamental and still largely open problem is the understanding of the long time behaviorExpand
Entropy decay in the Swendsen-Wang dynamics
We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that hasExpand
On the two-dimensional dynamical Ising model in the phase coexistence region
We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL, in the absence of an external field and at large inverse temperature β. We firstExpand
The Ising model on trees: boundary conditions and mixing time
TLDR
This work shows that the mixing time on an n-vertex regular tree with (+) boundary remains O(n log n) at all temperatures (in contrast to the free boundary case), and shows that this bound continues to hold in the presence of an arbitrary external field. Expand
Mixing Times of Critical Two‐Dimensional Potts Models
We study dynamical aspects of the q-state Potts model on an n × n box at its critical βc(q). Heat-bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that circumvent low-temperatureExpand
Information percolation and cutoff for the stochastic Ising model
We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties ofExpand
Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability
We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie–Weiss Model. For β < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarityExpand
Some New Results on the Kinetic Ising Model in a Pure Phase
AbstractWe consider a general class of Glauber dynamics reversible with respect to the standard Ising model in ℤd with zero external field and inverse temperature β strictly larger than the criticalExpand
Random-cluster dynamics in Z 2
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paperExpand
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