INFINITE-RANGE MEAN-FIELD PERCOLATION - TRANSFER-MATRIX STUDY OF LONGITUDINAL CORRELATION LENGTH

Two infinite-range directed percolation models, equivalent also to epidemic models, are considered for a finite population (finite number of sites) N at each "time" (directed axis) step. The general features of the transfer matrix spectrum (evolution operator spectrum for the epidemic) are studied numerically, and compared with analytical predictions in the limit N = infinity. One of the models is devised to allow numerical results to be obtained for N as high as nearly 800 for the largest longitudinal percolation correlation length (relaxation time for epidemic). The finite-N behavior of this correlation length is studied in detail, including scaling near the percolation transition, exponential divergence (with N) above the percolation transition, as well as other noncritical and critical-point properties.