Absorbing-state phase transitions: exact solutions of small systems

TL;DR

This paper derives exact results for absorbing-state phase transitions in small systems, providing highly accurate critical properties and exponents for models like the contact process and pair contact process.

Contribution

It introduces a method to precisely determine critical properties of absorbing-state phase transitions using exact quasistationary distributions for small systems.

Findings

Critical parameters estimated with better than 0.1% accuracy.

Accurate critical exponents for the contact process and pair contact process.

Validation of small system analysis for phase transition characterization.

Abstract

I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for the pair contact process.