A simple renormalization flow for FK-percolation models

TL;DR

This paper introduces a concrete renormalization flow for FK-percolation models, linking perturbations of critical limits to stationary distributions of simple Markov processes on discrete graphs, applicable in any dimension.

Contribution

It provides a new, explicit construction of renormalization flows for FK-percolation models that connects critical perturbations to Markov process stationary distributions.

Findings

Defines a concrete renormalization flow for FK-percolation models.

Links critical perturbations to stationary distributions of Markov processes.

Applicable in any spatial dimension.

Abstract

We present a setup that enables to define in a concrete way a renormalization flow for the FK-percolation models from statistical physics (that are closely related to Ising and Potts models). In this setting that is applicable in any dimension of space, one can interpret perturbations of the critical (conjectural) scaling limits in terms of stationary distributions for rather simple Markov processes on spaces of abstract discrete weighted graphs.