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, pc=0.30250.0010, and dominant critical exponents =1.210.05, for the mean cluster size; =0.820.03 and 1/=0.450.02 for the percolation probability in the thermal and field directions respectively; and a gap exponent of =2.030.06. We find a thermal-correction exponent 1=0.550.15 and a field correction of =0.30.1. We also calculate some universal critical-amplitude ratios.
ASJC Scopus subject areas
- Condensed Matter Physics