Burkhardt T W, Guim I
Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt B):5833-8. doi: 10.1103/physreve.59.5833.
The confinement free energy of a long, flexible, self-avoiding polymer chain, fluctuating in d spatial dimensions in an infinitely long cylindrical tube with diameter L, is given by DeltaF approximately Ak(B)TL(-1)R(parallel) for R(parallel)>>L. Here R(parallel) is the length of tube occupied by the chain, and A is a universal amplitude. We show how to determine DeltaF and R(parallel) from the correlation length xi(L)(t) of the n-vector model of magnetism in the limit n-->0, defined on the cylindrical volume, near the critical temperature t(c)(L) where xi(L) diverges. Using this correspondence, we estimate A in two dimensions from transfer-matrix data for self-avoiding walks on strips of width L with free, critically absorbing, and periodic boundaries. Our results for the universal amplitudes A and B approximately LR(-1)(parallel)<w(2)>, where w is the winding number, are in excellent agreement with Monte Carlo simulations of Frauenkron, Causo, and Grassberger for strips with periodic boundaries.
在直径为(L)的无限长圆柱形管中，在(d)维空间中波动的长而柔性的自回避聚合物链的受限自由能，对于(R_{∥}>>L)，由(\Delta F\approx Ak_{B}TL^{-1}R_{∥})给出。这里(R_{∥})是链占据的管的长度，(A)是一个普适振幅。我们展示了如何在(n\to0)的极限下，从定义在圆柱体积上、接近临界温度(t_{c}(L))（此时(\xi_{L})发散）的磁性(n)矢量模型的关联长度(\xi_{L}(t))来确定(\Delta F)和(R_{∥})。利用这种对应关系，我们根据宽度为(L)、具有自由、临界吸收和周期性边界的条带上自回避行走的转移矩阵数据，估计二维中的(A)。我们对于普适振幅(A)和(B\approx LR_{∥}^{-1}\langle w^{2}\rangle)（其中(w)是缠绕数）的结果，与Frauenkron、Causo和Grassberger对具有周期性边界的条带的蒙特卡罗模拟结果非常吻合。
