Non mean-field behavior of the contact process on scale-free networks

TL;DR

This paper investigates the contact process on scale-free networks, revealing non-mean-field critical behavior and emphasizing the importance of finite size effects in understanding phase transitions.

Contribution

It demonstrates that the contact process on scale-free networks exhibits non-trivial critical behavior not captured by mean-field theory, highlighting the role of finite size effects.

Findings

Finite size effects are significant in the contact process on scale-free networks.

The critical exponents depend on the network structure.

Mean-field theory fails to fully describe the critical behavior.

Abstract

We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a non-trivial critical behavior that cannot be quantitatively accounted for by mean-field theory.