Classical statistical mechanics of the sine-Gordon andφ4chains. Static properties

We present and discuss the classical statistical mechanics of the static properties associated with a discretized sine-Gordon and ${\phi }^4$ system by a numerical solution of the transfer-integral equation. The approximate replacement of the transfer-integral equation by a pseudo-Schrödinger equation is also considered to clarify the range of validity of this approach and of the associated WKB approximation. On this basis as well as low- and high-temperature perturbative expansions, it becomes possible to identify those thermodynamic properties and static form factors which are sensitive to or even dominated by the kinks. It is found that clear-cut kink effects are not only restricted to particular properties and to low and intermediate temperatures, but also, for the case of static form factors, to very small wave numbers.