Field theory of Ising percolating clusters

TL;DR

This paper develops an integrable field theory to describe the percolation transition of up-spin clusters in a 2D Ising model, revealing a non-perturbative mechanism for percolation without thermodynamic singularities.

Contribution

It introduces a novel integrable field theory framework for Ising percolation and extends analysis to the Kertesz line with Coniglio-Klein droplets.

Findings

Percolation threshold described by an integrable field theory

Identification of a non-perturbative transition mechanism

Extension of analysis to the Kertesz line with droplets

Abstract

The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable field theory and identify the non-perturbative mechanism which allows the percolative transition in absence of thermodynamic singularities. The analysis is extended to the Kertesz line along which the Coniglio-Klein droplets percolate in a positive magnetic field.