The analysis of Polyakov loop and spin correlators in finite volumes

TL;DR

This paper derives an analytic expression for Polyakov loop correlation functions using transfer matrix formalism, comparing results in 2D Ising model and finite temperature SU(2) gauge theory, revealing similar scaling and a volume-independent Debye mass near the critical point.

Contribution

It introduces an analytic approach to compute Polyakov loop correlators and investigates their behavior in different models and volume conditions.

Findings

Leading matrix element shows similar scaling in both models.

Debye screening mass approximately 4 near the critical point, volume-independent.

Eigenvalue contributions beyond the mass gap are analyzed.

Abstract

We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye screening mass $~\mu_D/T\approx4~$, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.