A Monte Carlo method for critical systems in infinite volume: the planar Ising model

Understand

In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume.

• The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices.
• It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it.
• We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction.