On statistical thermodynamics of multicomponent systems II

The equivalent neighbour (EN) model of interacting continuous spherically symmetric spins with the length equal or smaller than unity is solved exactly for all values of the spin dimensionality, D. A surprising result is that only for D 628 the system undergoes phase transitions at temperatures lower than those of the EN model of interacting spins with the hypercubic symmetry. In the D → ∞ limit the equation of state in zero field is derived analytically and gives the Landau type behaviour in the whole range of temperatures.