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arXiv · 0709.3774

Absorbing-state phase transitions: exact solutions of small systems

Ronald Dickman
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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.

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Ronald Dickman. 2007-09-24. Absorbing-state phase transitions: exact solutions of small systems. https://doi.org/10.1103/physreve.77.030102

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