2001/01/31 by P. Frojdh, PER FRÖJDH, M. Howard +3
Mathematics · Physics and Astronomy · #Critical dimension #Critical exponent #Critical phenomena #Directed percolation #Percolation (cognitive psychology) #Percolation critical exponents #Phase transition #Random Matrices and Applications #Renormalization group #Scaling #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0217979201004526
published as Int. J. Mod. Phys. B 15, 1761-1797 (2001) · 37 pages (including figures); journal-ref + ref added
openalex publication_date 2001/05/20 · arxiv created 2001/07/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of these models, we devote the main part of this review to analyzing the impact of walls on their critical behavior. We discuss the possible boundary universality classes for the DP and BARW models, which can be described by a general scaling theory which allows for two independent surface exponents in addition to the bulk critical exponents. Above the upper critical dimension d c , we review the use of mean field theories, whereas in the regime d<d c , where fluctuations are important, we examine the application of field theoretic methods. Of particular interest is the situation in d=1, which has been extensively investigated using numerical simulations and series expansions. Although DP and BARW fit into the same scaling theory, they can still show very different surface behavior: for DP some exponents are degenerate, a property not shared with the BARW model. Moreover, a "hidden" duality symmetry of BARW in d=1 is broken by the boundary and this relates exponents and boundary conditions in an intricate way.