Phase transitions with infinitely many absorbing states in complex networks

TL;DR

This paper investigates the phase transition properties of the threshold contact process (TCP) with infinitely many absorbing states on complex networks, revealing universal critical behavior similar to the contact process (CP) across different network types.

Contribution

The study demonstrates that TCP exhibits the same critical properties as CP in complex networks, suggesting universality in absorbing-state phase transitions regardless of the number of absorbing states.

Findings

TCP and CP share the same critical exponents in complex networks

Critical behavior depends only on local interactions, not on the number of absorbing states

Universality class of TCP and CP in complex networks is identified

Abstract

We instigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite size scaling exponents characterizing the transition are obtained in a heterogeneous mean field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process (CP), which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.