Perturbation theory in systems with long-range potential

A one-dimensional model with interaction energy $E=-I\sum_{i\not=j} e^{-\gamma(|i-j|-1)} \mu_i \mu_j$ of a definite configuration of spins is considered. A perturbation theory for large $\gamma$ is developed, the zeroth approximation being the model with only nearest-neighbor interaction. It is shown that at large $\gamma$ the free energy can be represented by a series in powers of $e^{-\gamma}$. The values of $\gamma$ for which this expansion is valid are found. The possibility of applying the method to two- and three-dimensional systems is considered.