Abstract
A replica trick is used to map the problem of directed polymers into a quantum mechanics problem ofn-body bound states. This bound-state problem is then treated using a self-consistent method of Hartree-Fock. Ford=2, the exact result of the DP exponents is reproduced; and for complex DP, the ground-state energyE n∼ n2 is found, confirming previous numerical results.
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Zhang, YC. Directed polymers in Hartree-Fock approximation. J Stat Phys 57, 1123–1128 (1989). https://doi.org/10.1007/BF01020051
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DOI: https://doi.org/10.1007/BF01020051