Kim Jin Min
Department of Physics and Research Institute for the Origin of Matter and the Evolution of Galaxies, Soongsil University, Seoul 156-743, Korea.
Phys Rev E. 2016 Dec;94(6-1):062149. doi: 10.1103/PhysRevE.94.062149. Epub 2016 Dec 29.
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.
描述了4 + 1维随机势中的零温定向聚合物。聚合物最低能量的涨落ΔE(t)随聚合物长度t按t^β变化，其中β = 0.159 ± 0.007，并且在饱和时ΔE遵循ΔE(L)∼L^α，α = 0.275 ± 0.009，这里L是系统尺寸。动态指数z≈1.73由z = α/β得出。指数的估计值很好地满足标度关系α + z = 2。我们还监测了聚合物的端到端距离并独立得到z。我们的结果表明，Kardar-Parisi-Zhang方程的上临界维度高于d = 4 + 1维。
