Bond percolation in a square lattice in presence of a 'magnetic field'

Abstract

The authors present a calculation of the bond percolation problem in a square lattice in presence of a 'magnetic field', using the position space renormalisation group and cells of dimension b*b, where b runs from 2 up to 5. Due to symmetry, the calculation splits into two parts, one determining the 'thermal' exponent nu and the other, the 'magnetic' exponent eta . For the largest cell in each case, one gets nu =1.355 (b=5) and eta =0.244 (b=4), in good agreement with series results of Dunn et al. (1975). Comments are made on the extrapolation of the results to b= infinity .