title: Zero-temperature directed polymer in random potential in 4+1 dimensions.
abstract: Zero-temperature directed polymer in random potential in 4+1 dimensions is described. The fluctuation ΔE(t) of the lowest energy of the polymer varies as t^{β} with β=0.159±0.007 for polymer length t and ΔE follows ΔE(L)∼L^{α} at saturation with α=0.275±0.009, where L is the system size. The dynamic exponent z≈1.73 is obtained from z=α/β. The estimated values of the exponents satisfy the scaling relation α+z=2 very well. We also monitor the end to end distance of the polymer and obtain z independently. Our results show that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than d=4+1 dimensions.
authors.affiliation: Department of Physics and Research Institute for the Origin of Matter and the Evolution of Galaxies, Soongsil University, Seoul 156-743, Korea.
authors.forename: Jin Min
authors.initials: JM
authors.lastname: Kim