Using transfer-matrix methods, we have investigated numerically the probability distributions that govern geometric and free-energy fluctuations in the (1+1)-dimensional directed polymer subject to quenched, uncorrelated Gaussian disorder. Exhaustive averaging, over many realizations of the random energy landscape, have permitted us to observe scaling of the third cumulant of the free energy as predicted by Kardar [Phys. Rev. Lett. 55, 2235 (1985)], to address issues concerning finite-size effects, and to discern the asymmetric form of the free-energy probability distribution. In addition, we have determined precisely the amplitudes of various transverse moments in order to compare to recent estimates of Bouchaud and Orland [J. Stat. Phys. 61, 877 (1990)].

• Received 17 June 1991

DOI:https://doi.org/10.1103/PhysRevA.44.R3415