An efficient transfer matrix technique is introduced to study directed optimal paths in two and three dimensions. The roughness exponent [Formula Presented] is 0.6325±0.0007 for the two-dimensional case and [Formula Presented] for the three-dimensional one, in agreement with the recent conjecture [Formula Presented], where [Formula Presented] and [Formula Presented] are the correlation length exponents of directed percolation. Exactly solvable examples are also analyzed. © 1996 The American Physical Society.

Optimal path and directed percolation

Caldarelli G.;Maritan A.;
1996-01-01

Abstract

An efficient transfer matrix technique is introduced to study directed optimal paths in two and three dimensions. The roughness exponent [Formula Presented] is 0.6325±0.0007 for the two-dimensional case and [Formula Presented] for the three-dimensional one, in agreement with the recent conjecture [Formula Presented], where [Formula Presented] and [Formula Presented] are the correlation length exponents of directed percolation. Exactly solvable examples are also analyzed. © 1996 The American Physical Society.
1996
53
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3728440
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