  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.
