TY - JOUR

T1 - Renormalization group, scaling and universality in spanning probability for percolation

AU - Hovi, J. P.

AU - Aharony, Amnon

N1 - Funding Information:
The calculations has been made possible by generous computer resources from the Center of Scientific Computing, Finland. We also thank D. Stauffer for critical reading of the full manuscript, M.E. Fisher for a discussion, and V. Privman for sending useful references. J.-P.H. gratefully acknowledges financial support from the Neste Foundation, Emil Aaltonen Foundation, and the Foundation of Financial Aid of Helsinki University of Technology. The work at Tel Aviv was also supported by a grant from the German-Israeli Foundation (GIF).

PY - 1995/11/15

Y1 - 1995/11/15

N2 - The spanning probability function for percolation is discussed using ideas from the renormalization group theory. We find that, apart from a few scale factors, the scaling functions are determined by the fixed point, and therefore are universal for every system with the same dimensionality, spanning rule, aspect ratio and boundary conditions, being independent of lattice structure and (finite) interaction length. This yields general results concerning the finite-size corrections and other corrections to scaling in general dimensions. For the special case of the square lattice with free boundaries, this theory, combined with duality arguments, give strong relations among different derivatives of the spanning function with respect to the scaling variables, thus yielding several new universal amplitude ratios and allowing systematic study of the corrections to scaling. The theoretical predictions are numerically confirmed with excellent accuracy.

AB - The spanning probability function for percolation is discussed using ideas from the renormalization group theory. We find that, apart from a few scale factors, the scaling functions are determined by the fixed point, and therefore are universal for every system with the same dimensionality, spanning rule, aspect ratio and boundary conditions, being independent of lattice structure and (finite) interaction length. This yields general results concerning the finite-size corrections and other corrections to scaling in general dimensions. For the special case of the square lattice with free boundaries, this theory, combined with duality arguments, give strong relations among different derivatives of the spanning function with respect to the scaling variables, thus yielding several new universal amplitude ratios and allowing systematic study of the corrections to scaling. The theoretical predictions are numerically confirmed with excellent accuracy.

UR - http://www.scopus.com/inward/record.url?scp=58149322417&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(95)00272-9

DO - 10.1016/0378-4371(95)00272-9

M3 - Article

AN - SCOPUS:58149322417

SN - 0378-4371

VL - 221

SP - 68

EP - 79

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-3

ER -