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Ising Model on the Torus and PCA Dynamics: Reversibility, Irreversibility, and Fast Tunneling

  • Carlo Lancia
  • Benedetto ScoppolaEmail author
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)

Abstract

In this chapter, we present a class of PCA (Probabilistic Cellular Automata) that can be used for approximate sampling the Gibbs measure. We list a series of results about them, restricting the discussion to the nearest-neighbor Ising model. For both the weakly and strongly coupled spins, we show how it is possible to explicitly evaluate the accuracy of our approximation scheme. Moreover, in the strong coupling regime (low temperature), we show how our procedure may drastically improve the known results about the convergence of the system to the stationary distribution. An important ingredient in this context is the use of an irreversible dynamics, which let new interesting states (the so-called Ising waves) arise.

Keywords

PCA Irreversibility Ising model Tunneling 

Notes

Acknowledgements

We thank the organizers of the workshop “Probabilistic Cellular Automata: Theory, Applications and Future Perspectives” (Eurandom 2013, TU Eindhoven) for the possibility to share ideas on this new and promising subject.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Medical Statistics and BioinformaticsLeiden University Medical CenterLeidenThe Netherlands
  2. 2.Dipartimento di MatematicaUniversità di Roma: Tor VergataRomaItaly

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