Finite temperature correlation functions of the sine--Gordon model

TL;DR

This paper applies the Method of Random Surfaces to compute finite-temperature correlation functions in the integrable sine-Gordon model, providing reliable non-perturbative data and exact multi-point results.

Contribution

It introduces a novel application of the Method of Random Surfaces for finite-temperature correlation functions in the sine-Gordon model, including exact N-point functions.

Findings

Validated MRS results against known analytical limits.

Provided non-perturbative data where traditional methods fail.

Derived exact N-point correlation functions at finite temperature.

Abstract

The sine-Gordon model serves as a foundational $1+1$-dimensional quantum field theory with numerous applications in condensed matter physics. Despite its integrability, characterizing its finite-temperature behavior remains a significant theoretical challenge. Here we use the previously developed Method of Random Surfaces (MRS) to evaluate two-point and higher-order correlation functions. We cross-check these results with known analytical limits, demonstrating that the MRS provides reliable, non-perturbative data in intermediate regimes where traditional form-factor expansions and semiclassical methods are inapplicable. Furthermore, we derive an exact result for arbitrary $N$-point functions satisfying an appropriate selection rule, providing a direct computational method for complex multi-point observables at finite temperature. We also characterize the non-Gaussianity of correlations and demonstrate that the results align with intuitive theoretical expectations.