Scaling Limit for the Incipient Spanning Clusters

TL;DR

This paper discusses the formulation of the continuum scaling limit for critical percolation models in low dimensions, emphasizing conformal invariance and universality in the critical behavior.

Contribution

It proposes a mathematical framework for directly describing the continuum limit of critical percolation models in low dimensions, highlighting conformal invariance.

Findings

Expected strict conformal invariance in the continuum limit

Framework facilitates analysis of universality and critical phenomena

Links to field theories in statistical physics

Abstract

Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the direct description of the limiting continuum theory. The resulting structure is expected to exhibit strict conformal invariance, and facilitate the mathematical discussion of questions related to universality of critical behavior, conformal invariance, and some relations with a number of field theories.