Phase transition in the isotropic m-vector model on a random graph

The thermodynamics of a phase transition is investigated within an isotropic m-vector model on a graph with sparse random connections. This model adequately describes superconductivity and superfluidity (m=2), Heisenberg magnets (m=3), and some structural transitions in different systems with macroscopic disorder (gels, composites, and porous media). It is demonstrated that the phase transition is characterized by classical effective-field anomalies. The thermodynamics of the phase transition is also analyzed in terms the proposed model at low temperatures. The dependences of the thermodynamic parameters on the external field, the mean coordination number, and the dimension of the order parameters are determined.