Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional $(q+1)$-state clock model

TL;DR

This paper uses Monte Carlo simulations to compute operator product expansion coefficients at criticality in the 3D XY universality class, comparing results with conformal bootstrap estimates to verify consistency.

Contribution

It provides high-precision Monte Carlo estimates of OPE coefficients for the 3D XY universality class, validating conformal bootstrap results.

Findings

Monte Carlo simulations up to L=960 lattice size.

OPE coefficients consistent with conformal bootstrap estimates.

Enhanced understanding of critical phenomena in 3D XY universality class.

Abstract

We simulate the improved $(q+1)$-state clock model on the simple cubic lattice at the critical point on lattices of a linear size up to $L=960$. We compute operator product expansion (OPE) coefficients for the three-dimensional XY universality class. These are compared with highly accurate estimates obtained by using the conformal bootstrap method. We find that the results are consistent.