Critical exponents of domain walls in the two-dimensional Potts model

TL;DR

This paper investigates the critical behavior of spin cluster domain walls in the 2D Potts model, introducing a transfer matrix method for non-integer Q and deriving a series of critical exponents related to domain wall crossings.

Contribution

It develops a transfer matrix approach for analyzing spin clusters in the 2D Potts model for non-integer Q and identifies new critical exponents for domain wall crossings.

Findings

Derived an infinite series of critical exponents for domain walls.

Formulated a transfer matrix technique for non-integer Q.

Connected crossing events to conformal correlation functions.

Abstract

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the insertion of l_1 thin and l_2 thick domain walls.