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Block scaling in the directed percolation universality class

Published 7 November 2008 Published under licence by IOP Publishing Ltd
, , Citation Gunnar Pruessner 2008 New J. Phys. 10 113003 DOI 10.1088/1367-2630/10/11/113003

1367-2630/10/11/113003

Abstract

The universal behaviour of the directed percolation universality class is well understood—both the critical scaling and the finite size scaling. This paper focuses on the block (finite size) scaling of the order parameter and its fluctuations, considering (sub-)blocks of linear size l in systems of linear size L. The scaling depends on the choice of the ensemble, as only the conditional ensemble produces the block-scaling behaviour as established in equilibrium critical phenomena. The dependence on the ensemble can be understood by an additional symmetry present in the unconditional ensemble. The unconventional scaling found in the unconditional ensemble is a reminder of the possibility that scaling functions themselves have a power-law dependence on their arguments.

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10.1088/1367-2630/10/11/113003