Phase ordering and universality for continuous symmetry models on graphs

We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with N = 3 and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one found on usual lattices. The exponent a. for the integrated response function and the exponent z, describing the growing length, are related to the large scale topology of the networks through the spectral dimension and the fractal dimension alone, by means of the same expressions as are provided by the analytic solution of the N -> infinity 8 limit. This suggests that the large N value of these exponents could be exact for every N >= 2.