Exact Thermodynamics of the Double sinh-Gordon Theory in 1+1-Dimensions

TL;DR

This paper provides an exact thermodynamic analysis of the 1+1-dimensional double sinh-Gordon model, revealing quasi-exact solvability at certain temperatures and matching simulation results, with links to related models.

Contribution

It introduces an exact solution approach for the thermodynamics of the double sinh-Gordon theory, including partition functions and correlations, at specific temperatures.

Findings

Exact partition function calculation at multiple temperatures

Good agreement with Langevin simulations

Connections established with Landau-Ginzburg and double sine-Gordon models

Abstract

We study the classical thermodynamics of a 1+1-dimensional double-well sinh-Gordon theory. Remarkably, the Schrodinger-like equation resulting from the transfer integral method is quasi-exactly solvable at several temperatures. This allows exact calculation of the partition function and some correlation functions above and below the short-range order (``kink'') transition, in striking agreement with high resolution Langevin simulations. Interesting connections with the Landau-Ginzburg and double sine-Gordon models are also established.