Phase ordering and universality for continuous symmetry models on graphs

TL;DR

This paper investigates phase-ordering kinetics in continuous symmetry models on graphs, revealing that their scaling behaviors depend on network topology and are consistent across different N values, similar to lattice cases.

Contribution

It demonstrates that the scaling exponents in O(N) models on graphs are determined by spectral and fractal dimensions, extending known lattice results to complex networks.

Findings

Scaling exponents relate to spectral and fractal dimensions.

Scaling behaviors are analogous to those on regular lattices.

Large N exponents may be exact for all N.

Abstract

We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with 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 inifnite N limit. This suggests that the large N value of these exponents could be exact for every N.