Summary: Physica A 295 (2001) 128131
Directed percolation, fractal roots and the
, S.R. Dahmenb;
, H. Hinrichsenc
aInstitute for Theoretical Physics, Universitat zu Koln, Zulpicher Stra e 77, D-50937 Cologne, Germany
bInstituto de FĆsica, Universidade Federal do Rio Grande do Sul, C. P. 15051, 91501-970 Porto Alegre,
cPhysics Department, Universitat Duisburg, Lotharstra e 1, D-47048 Duisburg, Germany
In the directed percolation model we consider the probability p of having an open bond as a
complex parameter. We show that the roots of the survival probability PN (p) for a square lattice
of N rows distribute themselves in a fractal manner in the complex p-plane. These roots have
an accumulation point on the real axis which coincides with the critical probability pc = 0:6447.
c 2001 Elsevier Science B.V. All rights reserved.
PACS: 05.70.Fh; 64.60.Ak; 02.30.Dk
Keywords: Phase transitions; Percolation model; Complex Analysis
Spreading phenomena abound in nature in such diverse situations as forest ˙res,