Thermodynamics of Classical One-dimensional Klein-Gordon Lattice Model

TL;DR

This paper investigates the thermodynamic properties of the classical one-dimensional Klein-Gordon lattice model using an exact method in the thermodynamic limit, providing detailed analysis of various physical quantities and their scaling behaviors.

Contribution

It applies the cluster variation method with linear response theory to derive exact thermodynamic properties of the Klein-Gordon lattice model in the thermodynamic limit.

Findings

Derived exact expressions for density matrices and correlation functions.

Analyzed scaling behavior and determined scaling powers at different temperatures.

Assessed the accuracy of the projective truncation approximation for the $\

Abstract

In this paper, we study the thermodynamical properties of the classical one-dimensional Klein-Gordan lattice model ($n \ge 2$) by using the cluster variation method with linear response theory. The results of this method are exact in the thermodynamical limit. We present the single site reduced density matrix $\rho^{(1)}(z)$, averages such as $\langle z^2 \rangle$, $\langle |z^n|\rangle$, and $\langle (z_1-z_2)^2\rangle$, the specific heat $C_v$, and the static correlation functions. We analyzed the scaling behavior and obtained the exact scaling powers of these quantities in the low and high temperaures. Using these results, we gauge the accuracy of the projective truncation approximation for $\phi^{4}$ lattice model.