Exact thermodynamics of the double sinh-Gordon theory in 1+1 dimensions

Abstract

We study the classical thermodynamics of a (1+1)-dimensional double-well sinh-Gordon theory. Remarkably, the Schrödinger-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.