2007/06/30 by Gunnar Pruessner · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Block (permutation group theory) #Complex Systems and Time Series Analysis #Directed percolation #Percolation critical exponents #Renormalization group #Scaling #Scaling law #Statistical Mechanics and Entropy #Theoretical and Computational Physics #Universality (dynamical systems) #Widom scaling #cond-mat.stat-mech
paper · pdf · doi:10.1088/1367-2630/10/11/113003
published in New Journal of Physics 10(11), 113003 (IOP Publishing) · 14 pages, 5 figures, IOP style
arxiv created 2008/09/19 · openalex publication_date 2008/11/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.