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.;
1996
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.File in questo prodotto:
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