Crossover between short- and long-range interactions in the one-dimensional Ising model

Abstract

The authors consider the one-dimensional Ising model which besides the interaction of nearest neighbours includes a long-range term. The latter is ferromagnetic while the nearest-neighbour interaction can have any sign. The crossover between short- and long-range interactions when varying the Hamiltonian parameters is analysed for such a model. For some values of the antiferromagnetic short-range interaction the transition from a ferro- to paramagnetic state is of first order. At the tricritical point where the transition order changes from second to first they obtain classical tricritical exponents. For a ferromagnetic short-range interaction the Curie temperature surpasses the transition temperature of the long-range model.