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Directed percolation in 3+1 dimensions

1988; American Physical Society; Volume: 37; Issue: 13 Linguagem: Inglês

10.1103/physrevb.37.7529

1095-3795

Joan Adler, Jorge Berger, J. A. M. S. Duarté, Yigal Meir,

Complex Network Analysis Techniques

Directed percolation in four dimensions is of direct physical relevance to the world with three space and one time dimension. We present a comprehensive analysis of recently extended series for the moments of the cluster-size distribution and for the percolation probability in a ``field'' on the hypercubic lattice. We find a critical threshold, ${p}_{c}$=0.3025\ifmmode\pm\else\textpm\fi{}0.0010, and dominant critical exponents \ensuremath{\gamma}=1.21\ifmmode\pm\else\textpm\fi{}0.05, for the mean cluster size; \ensuremath{\beta}=0.82\ifmmode\pm\else\textpm\fi{}0.03 and 1/\ensuremath{\delta}=0.45\ifmmode\pm\else\textpm\fi{}0.02 for the percolation probability in the thermal and field directions respectively; and a gap exponent of \ensuremath{\Delta}=2.03\ifmmode\pm\else\textpm\fi{}0.06. We find a thermal-correction exponent ${\ensuremath{\Delta}}_{1}$=0.55\ifmmode\pm\else\textpm\fi{}0.15 and a field correction of \ensuremath{\Omega}=0.3\ifmmode\pm\else\textpm\fi{}0.1. We also calculate some universal critical-amplitude ratios.