Numerical Determination of Boundary Condition Changing Operators

TL;DR

This paper introduces a numerical method based on SLE(6; 6) to determine boundary condition changing operators in statistical models, exemplified by the Abelian Sandpile Model, revealing the conformal dimension of the sink operator.

Contribution

A novel numerical approach using SLE(6; 6) to identify boundary operators in statistical models, validated on the Abelian Sandpile Model.

Findings

Conformal dimension of the sink operator is nearly 0.

The sink operator is likely the logarithmic partner of the identity.

Method successfully characterizes boundary operators in complex models.

Abstract

A new numerical method to determine the boundary condition changing (bcc) operators in the statistical models is introduced. This method is based on a variant of Schramm-Loewner Evolution (SLE), namely SLE(\kappa; \rho). As a prototype, Abelian Sandpile Model (ASM) with a sink on some point on the boundary is considered. Using this method we study the bcc operator corresponding to sink. It is numerically shown that the conformal dimension of the this operator is nearly 0. The most suitable candidate for this operator is the logarithmic partner of the unity operator, as it has been conjectured theoretically.