Numerical study on Schramm-Loewner Evolution in nonminimal conformal field theories

TL;DR

This paper numerically investigates Schramm-Loewner Evolution (SLE) in non-minimal conformal field theories by analyzing interfaces in Z(N) spin models at criticality, extending SLE applications beyond minimal CFTs.

Contribution

It provides the first numerical analysis of SLE in non-minimal CFTs, specifically for Z(N) models, confirming theoretical predictions about interface fractal dimensions.

Findings

Fractal dimensions of interfaces match theoretical predictions

SLE candidates are identified for non-minimal CFTs

Results extend SLE applicability to models with additional symmetries

Abstract

The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only conformal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a Z_N symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.