Conformal Bootstrap Analysis for Single and Branched Polymers

TL;DR

This paper applies the conformal bootstrap determinant method to analyze critical exponents of single and branched polymers across various dimensions, confirming dimensional reduction relations.

Contribution

It introduces a small determinant approach within conformal bootstrap to compute polymer critical exponents and verifies dimensional reduction for branched polymers.

Findings

Critical exponents for polymers in various dimensions obtained.

Dimensional reduction of branched polymers to Yang-Lee edge singularity confirmed.

Method provides a new computational approach for polymer critical phenomena.

Abstract

The determinant method in the conformal bootstrap is applied for the critical phenomena of a single polymer in arbitrary $D$ dimensions. The scale dimensions (critical exponents) of the polymer ($2< D \le 4$) and the branched polymer ($3 < D \le 8$) are obtained from the small determinants. It is known that the dimensional reduction of the branched polymer in $D$ dimensions to Yang-Lee edge singularity in $D$-$2$ dimensions holds exactly. We examine this equivalence by the small determinant method.