Statistical mechanics of nonlinear Klein–Gordon chains: the φ8-chain and the Gaussian double-well model

We study the statistical mechanics of two models of nonlinear Klein–Gordon chain: the ‘φ8-chain’ with the single-site potential v(y)=a(y2−1)4, and the Gaussian double-well model with v(y)=12ky2+bexp(−12cy2) where a,b,c and k are positive constants. The thermodynamics of the classical chains is investigated by the transfer-integral equation technique and the pseudo-Schrödinger equation approximation. The results for the heat capacity, the displacement correlation function, and the wave-vector-dependent susceptibility are compared with those of the familiar φ4-chain. The partition functions of the quantum chains are calculated by the low-coupling effective potential method. The effects of quantum fluctuations on the low-temperature heat capacity are examined.