On Convergence to SLE$_6$ II: Discrete Approximations and Extraction of Cardy's Formula for General Domains

TL;DR

This paper proves the convergence of certain discrete models to SLE$_6$ and derives Cardy's Formula for general domains, advancing understanding of critical phenomena in statistical physics.

Contribution

It extends previous convergence results to general domains and provides a method to extract Cardy's Formula in these settings.

Findings

Convergence of exploration processes to SLE$_6$ in general domains

Derivation of Cardy's Formula for arbitrary domains

Framework for analyzing discrete models at criticality

Abstract

Following the approach outlined in [17], convergence to SLE$_6$ of the Exploration Processes for the correlated bond-triangular type models studied in [6] is established in [3] and the present work. In this second part, we focus on establishing Cardy's Formula for general domains.