Mean field and cavity analysis for coupled oscillator networks

Abstract

We study coupled oscillator spin systems on sparse, random graphs. In particular, we examine the recent conjecture of Ichinomiya on the equivalence of a sparsely connected oscillator network with ferromagnetic interactions to a fully connected network with disordered (i.e., randomly quenched) interactions. By restricting our investigation to a Hamiltonian case we can use the techniques of equilibrium statistical mechanics to compare these two models analytically including phase diagrams and the calculation of order parameters in the ordered phase. We complete our investigation by performing some Monte Carlo simulations to compare our theoretical predictions against.