Surface critical behavior in systems with nonequilibrium phase transitions

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American Physical Society

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d(c), with d(c)=4 (DP) and d(c)=2 (BARW), we use mean field-theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension d less than or equal to d(c), we use field theoretic methods to study the effects of fluctuations. As in the bulk, the field-theory suffers from technical difficulties associated with the presence of a second critical dimension. However, we are still able to analyze the phase diagrams for BARW in d = 1 and 2, which turn out to be very different from their mean field analog. Furthermore, for the case of BARW only (and not for DP), we find two independent surface beta(1) exponents in d = 1, arising from two distinct definitions of the order parameter. Using an exact duality transformation on a lattice BARW model in d = 1, we uncover a relationship between these two surface beta(1) exponents at the ordinary and special transitions. Many of our predictions are supported using Monte Carlo simulations of two different models belonging to the BARW universality class.

annihilating random-walks, kinetic critical phenomenon, reggeon, field-theory, monomer-dimer model, directed percolation, absorbing, states, universality class, series expansions, lattice, Physics
Howard, M ; Frojdh, P ; Lauritsen, KB, Jan 2000. "Surface critical behavior in systems with nonequilibrium phase transitions," PHYSICAL REVIEW E 61(1): 167-183. DOI: 10.1103/PhysRevE.61.167