Absorbing-state phase transitions: exact solutions of small systems.
I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary (QS) 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 betanu_(perpendicular)) with an accuracy of 0.06% or better; precise results are also obtained for the pair contact process. The QS distribution yields insights on the statistical entropy of these models. Preliminary application to a model in the stochastic sandpile class is also described.
Departamento de Física, ICEx, Universidade Federal de Minas Gerais, 30123-970, Belo Horizonte, Minas Gerais, Brazil. dickman@fisica.ufmg.br
Ronald
R
Dickman