Perfect sampling of -spin systems on via weak spatial mixing

  • Konrad Anand

    Queen Mary University of London, London, UK
  • Mark Jerrum

    Queen Mary University of London, London, UK
Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$  via weak spatial mixing cover
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Abstract

We present a perfect marginal sampler of the unique Gibbs measure of a spin system on . The algorithm is an adaptation of a previous “lazy depth-first” approach by the authors, but relaxes the requirement of strong spatial mixing to weak. Our result is a step towards methods of efficient sampling using only weak spatial mixing. The work exploits a classical result in statistical physics relating weak spatial mixing on to strong spatial mixing on squares. When the spin system exhibits weak spatial mixing, the run-time of our sampler is linear in the size of sample. Applications of note are the ferromagnetic Potts model at supercritical temperatures and the ferromagnetic Ising model with consistent non-zero external field at any non-zero temperature.

Cite this article

Konrad Anand, Mark Jerrum, Perfect sampling of -spin systems on via weak spatial mixing. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/195