Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-05-15
Acta Physica Slovaca 52 (2002) 505
Physics
Condensed Matter
Statistical Mechanics
9 pages, latex; talk presented at RG02; Proc. to appear in Acta Physica Slovaca (style files included)
Scientific paper
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d_c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d_c' = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues.
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