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

Abstract

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. We accurately reproduce planar two-, three- and four-point functions of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.

43 pages, 21 figures

References in corpus (2)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Thermal Behavior of Spin Clusters and Interfaces in two-dimensional Ising Model on Square Lattice

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• Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler
• Markov chain sampling of the $O(n)$ loop models on the infinite plane