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 similar to E(t) of the lowest energy of the polymer varies as t beta with beta = 0.159 +/- 0.007 for polymer length t and Delta E follows Delta E(L) similar to La at saturation with a = 0.275 +/- 0.009, where L is the system size. The dynamic exponent z approximate to 1.73 is obtained from z = alpha/beta. The estimated values of the exponents satisfy the scaling relation alpha + 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.