LONGITUDINAL CORRELATION LENGTH IN DIRECTED PERCOLATION AND RELATED MODELS: A POSSIBLE NEW SCALING MECHANISM

1991 ◽  
Vol 05 (08) ◽  
pp. 555-559 ◽  
Author(s):  
MALTE HENKEL ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Long Range ◽  
Correlation Length ◽  
Finite Size ◽  
Directed Percolation ◽  
Long Range Order ◽  
Finite Size Scaling ◽  
Asymptotic Behaviors ◽  
Longitudinal Correlation ◽  
Asymptotic Eigenvalue ◽  
Asymptotic Scaling

The finite-size scaling of the correlation length for directed and undirected systems is reviewed with emphasis on the asymptotic eigenvalue degeneracy associated with long-range order or long-range connectivity. The standard scaling mechanism for matching asymptotic behaviors on approach to criticality applies for Ising and other models. However, numerical evidence suggests that for directed percolation in 2D a modified formulation is appropriate, incorporating irrelevant-variable corrections in a new pattern of asymptotic scaling.

FINITE-SIZE SCALING FOR THE SPHERICAL MODEL WITH LONG-RANGE INTERACTION

1995 ◽  
Vol 09 (18) ◽  
pp. 1117-1121
Author(s):  
K. NOJIMA
Keyword(s):  
Critical Temperature ◽  
Long Range ◽  
Finite Size ◽  
Spherical Model ◽  
Critical Dimension ◽  
Finite Size Scaling ◽  
Range Interaction ◽  
Upper Critical Dimension ◽  
Size Scaling ◽  
Long Range Interaction

The finite-size scaling property of the correlation length for the spherical model with long-range interaction is examined above the critical temperature. The analysis is performed below the upper critical dimension.

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