Universality classes for the dynamic surface critical behavior of systems with relaxational dynamics

1994 ◽  
Vol 49 (4) ◽  
pp. 2846-2860 ◽  
Author(s):  
H. W. Diehl
Keyword(s):  
Critical Behavior ◽  
Dynamic Surface ◽  
Surface Critical Behavior ◽  
Universality Classes

scholarly journals The Theory of Boundary Critical Phenomena

1997 ◽  
Vol 11 (30) ◽  
pp. 3503-3523 ◽  
Author(s):  
H. W. Diehl
Keyword(s):  
Critical Phenomena ◽  
Critical Behavior ◽  
Short Distance ◽  
Universality Class ◽  
Field Theories ◽  
Group Method ◽  
Renormalization Group Method ◽  
Surface Critical Behavior ◽  
Universality Classes ◽  
Parameter Profile

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.

scholarly journals Surface Critical Behavior of Two-Dimensional Dilute Ising Models

1997 ◽  
Vol 89 (5-6) ◽  
pp. 1079-1085 ◽  
Author(s):  
W. Selke ◽  
F. Szalma ◽  
P. Lajkó ◽  
F. Iglói
Keyword(s):  
Critical Behavior ◽  
Ising Models ◽  
Two Dimensional ◽  
Surface Critical Behavior

scholarly journals Wavevector scaling, surface critical behavior, and wetting in the 2-d, 3-state chiral clock model

1987 ◽  
Vol 67 (3) ◽  
pp. 357-361 ◽  
Author(s):  
A. L. Stella ◽  
X. C. Xie ◽  
T. L. Einstein ◽  
N. C. Bartelt
Keyword(s):  
Critical Behavior ◽  
Clock Model ◽  
Surface Critical Behavior

scholarly journals DIRECTED PERCOLATION AND OTHER SYSTEMS WITH ABSORBING STATES: IMPACT OF BOUNDARIES

2001 ◽  
Vol 15 (12) ◽  
pp. 1761-1797 ◽  
Author(s):  
PER FRÖJDH ◽  
MARTIN HOWARD ◽  
KENT BÆKGAARD LAURITSEN
Keyword(s):  
Critical Behavior ◽  
Mean Field ◽  
Critical Dimension ◽  
Scaling Theory ◽  
Directed Percolation ◽  
Upper Critical Dimension ◽  
Duality Symmetry ◽  
Universality Classes ◽  
Absorbing States ◽  
The Impact

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.

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