The lifespan method as a tool to study criticality in absorbing-state phase transitions

TL;DR

The paper evaluates the lifespan method as a reliable numerical tool for analyzing critical phenomena in absorbing-state phase transitions, validating it against established methods and analytical results.

Contribution

It develops a finite-size scaling theory for the lifespan method and demonstrates its effectiveness for studying the contact process on lattices.

Findings

Lifespan method results agree with quasi-stationary simulations.

The method accurately measures critical points and exponents.

Validated for the contact process on 1D lattices.

Abstract

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [Phys. Rev. Lett. \textbf{111}, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasi-stationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasi-stationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices.