Thermodynamics of a vortex system in thin-layer semiconductors

We develop a method for estimating a classical partition function for a system of $N$ particles that reduces it to the partition function of a scalar field model of the sine-Gordon type. We find the free energy of a system of magnetic vortices in a thin-layer semiconductor and investigate its equilibrium properties in the leading order of the perturbation theory, which corresponds to a circle approximation for a particle system.