Thermodynamics of classical one-dimensional generalized nonlinear Klein–Gordon lattice model

We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein–Gordon lattice model (n ≥ 2) by using the cluster variation method with linear response theory. The results of this method are exact in the thermodynamic limit. We present the single-site reduced density ρ⁽¹⁾(z), averages such as 〈z²〉, 〈|zⁿ|〉, and 〈(z₁–z₂)²〉, the specific heat C_v, and the static correlation functions. We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures. Using these results, we gauge the accuracy of the projective truncation approximation for the ϕ⁴ lattice model.