Zero-temperature directed polymers in a random potential.
Zero-temperature directed polymers in a random potential.
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DOI：
10.1103/physreva.44.2345
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发表时间：
1991-08
期刊：
影响因子：
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通讯作者：
Jin Min Kim;M. Moore;A. Bray
中科院分区：
文献类型：
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作者：
Jin Min Kim;M. Moore;A. Bray
描述了在随机势中对定向聚合物模型的广泛模拟。T阶步的最低能量E的标准差ΔE(T)随tω变化，但文献中引用的ω在d=2+1和3+1中的值有很大的差异。在我们的模型中，我们能够改变一个参数-聚合物的弯曲能-影响ω的表观值，但是，如果考虑到标度的修正，那么我们发现ω是普遍的，d=2+1中的值为0.248±0.004，d=3+1中的ω=0.2±0.01.概率分布P(E，t)被发现为t→∞，P(E，t)de→P(A)da，其中a=(E-<；E>；)/ΔE.研究发现，标度函数P(A)是通用的，即与随机势分布的选择等细节无关，并且实际上在我们的数值精度内与弹道聚集模型中的等效高度分布相同。
Extensive simulations of a model of directed polymers in a random potential are described. The standard deviation ΔE (t) of the lowest energy E of walks of t steps varies as t ω, but there is a large spread in the values quoted in the literature for ω in d= 2+ 1 and 3+ 1. In our model we are able to vary a parameter—the bending energy of the polymer—that affects the apparent value of ω, but, if allowance is made for corrections to scaling, then we find that ω is universal with the value 0.248±0.004 in d= 2+ 1 and ω= 0.20±0.01 in d= 3+ 1. The probability distribution P (E, t) is found to scale as t→∞, P (E, t) dE→ P (a) da, where a=(E-< E>)/ΔE. The scaling function P (a) is investigated and found to be universal, ie, independent of such details as choice of distribution of the random potential, etc., and in fact identical to within our numerical accuracy to the equivalent distribution of heights in a model of ballistic aggregation.