Thermodynamic properties of a one-dimensional Heisenberg system with long-range interaction

The thermodynamic properties of one-dimensional systems with long-range exchange interaction between classical spins are considered. The transfer matrix method is used to calculate the state function, whose functional integral is transformed into an equivalent integral with nearest-neighbor interaction. At low temperatures, it is shown that with increasing range $\gamma^{-1}$ of the exchange interaction the contribution of the Bloch domain walls to the free energy decreases exponentially. The correlation lengths are obtained as functions of $\gamma^{-1}$.