Fermi partition functions of friendly walkers and pair connectedness of directed percolation

Non-crossing random walkers with attractive interactions called friendly wa lkers (FWs) are studied. A restriction on trajectories, which is analogous to Pauli's exclusion principle, is imposed and the Fermi partition function s are defined. We prove a theorem that the pair connectedness of the bond d irected percolation (DP) with bond concentration p is related to the Fermi grand partition function of FW if we set, the temperature T = -1/(k(B) ln p ) and the chemical potential mu = -i pi /lnp, where k(B) is the Boltzmann c onstant and i = root -1. The pure imaginary chemical potential means that t he DP transition can be regarded as a symmetry breaking of parity in the nu mber of FWs. As a corollary of the theorem, a new method is proposed for ca lculating the series expansion of the pair connectedness and percolation pr obability of DP using the low-temperature expansion data of FW.