Thermodynamics of a classical sine-Gordon field on finite support

The statistical mechanics of a sine-Gordon field on a finite-length support is studied by the functional integral method. Periodic boundary conditions are coherently imposed for both soliton and radiation components. The band spectrum of the small oscillations in the presence of the static soliton with different "kink number" is discussed for arbitrary length of the system and the correct infinite-length limit is obtained. The partition function is evaluated at low temperatures varying the length of the system, and the kink contribution to the free energy is dervied. Particular care is devoted to the correct treatment of the lower-band nontranslational modes in order to recover the "dilute gas approximation" for the infinite system. All corrections due to the finite dimension of the support are calculated and discussed.