Continuum limit of sine-Gordon andφ4chains by use of an effective potential

The effective potential previously introduced by the variational method is used to calculate thermodynamic quantities of quantum one-dimensional nonlinear fields in the weak-coupling approximation. The correct continuum limit is recovered both for integrable (sine-Gordon) and noninte- grable (${\phi }^4$) models. Good agreement is found with exact Bethe-ansatz results for the specific heat.