Towards Conformal Invariance and a Geometric Representation of the 2D Ising Magnetization Field

TL;DR

This paper investigates the continuum scaling limit of the critical 2D Ising magnetization field, establishing subsequential limits and exploring connections with FK cluster scaling limits, advancing the understanding of conformal invariance in statistical physics.

Contribution

It proves the existence of subsequential limits of the critical 2D Ising magnetization field and explores its relation to FK cluster scaling limits, contributing to conformal invariance studies.

Findings

Existence of subsequential limits for the 2D Ising magnetization field

Connections established between magnetization limits and FK cluster scaling

Progress in understanding conformal invariance in critical phenomena

Abstract

We study the continuum scaling limit of the critical Ising magnetization in two dimensions. We prove the existence of subsequential limits, discuss connections with the scaling limit of critical FK clusters, and describe work in progress of the author with C. Garban and C.M. Newman.