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Updated: May 13, 2026
08:12
An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data
Published on: February 16, 2024
Phase transitions with infinitely many absorbing states in complex networks
Renan S Sander1, Silvio C Ferreira, Romualdo Pastor-Satorras
1Departamento de Física, Universidade Federal de Viçosa, 36571-000 Viçosa, Minais Gerais, Brazil.
Summary
The threshold contact process (TCP) on complex networks shows universal critical behavior similar to the standard contact process. This universality in absorbing-state phase transitions depends on interaction locality, not the number of absorbing states.
Area of Science:
- Statistical Physics
- Network Science
- Complex Systems
Background:
- The threshold contact process (TCP) exhibits absorbing-state phase transitions with multiple absorbing states.
- Understanding phase transitions on complex networks is crucial for modeling various phenomena.
Purpose of the Study:
- To investigate the properties of the TCP on random complex networks.
- To determine the finite-size scaling exponents of the TCP transition.
- To compare theoretical approximations with simulation results.
Main Methods:
- Heterogeneous mean-field (HMF) approximation.
- Extensive numerical simulations.
- Analysis of heterogeneous scale-free networks.
Main Results:
- The TCP on complex networks displays critical properties identical to the standard contact process.
- Finite-size scaling exponents were calculated using HMF approximation and simulations.
- Critical exponents were found to be consistent across different network types and models.
Conclusions:
- The critical behavior of the contact process in HMF theory is a universal feature of absorbing-state phase transitions in complex networks.
- Universality depends on interaction locality and is independent of the number of absorbing states.
- The study contrasts this universality with epidemic models like susceptible-infected-susceptible (SIS) which belong to different universality classes.
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