无规受迫定向聚合物的自由能分布函数
Free-energy distribution functions for the randomly forced directed polymer
摘要：
我们研究了$1+1$ -维无规定向聚合物问题，即，弹性弦$ϕ(x)$受高斯随机势$V(ϕ,x)$的作用并被限制在一个平面内。我们主要集中在短尺度和有限温度的行为，这个问题所描述的短，但有限范围的无序相关$U(ϕ)$，并介绍两种类型的近似服从精确解。扩展无序势$V(ϕ,x) \approx V_0(x) + f(x) ϕ(x)$在短距离，我们研究了随机力（或拉金）问题与$V_0(x) = 0$以及移位随机力的问题，包括随机偏移$V_0(x)$，因此，这些模型仍然很好地定义在所有尺度。或者，我们分析谐波近似的相关器$U(ϕ)$在一个一致的方式。使用直接平均以及副本技术，我们推导出的分布函数${\cal P}_{L,y}(F)$和${\cal P}_L(F)$的自由能$F$的聚合物长度$L$固定（$ϕ(L) = y$）和自由边界条件上的位移场$ϕ(x)$，并确定平均位移放大器上的距离$L$。谐波近似的相关器的分析中遇到的不一致追溯到其非光谱相关器，我们讨论了如何实现这种近似在一个适当的方式，并提出了一个一般的标准，物理上可接受的混乱disorder discharators $U(ϕ)$。
英文摘要：
We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $ϕ(x)$ subject to a Gaussian random potential $V(ϕ,x)$ and confined within a plane. We mainly concentrate on the short-scale and finite-temperature behavior of this problem described by a short- but finite-ranged disorder correlator $U(ϕ)$ and introduce two types of approximations amenable to exact solutions. Expanding the disorder potential $V(ϕ,x) \approx V_0(x) + f(x) ϕ(x)$ at short distances, we study the random force (or Larkin) problem with $V_0(x) = 0$ as well as the shifted random force problem including the random offset $V_0(x)$; as such, these models remain well defined at all scales. Alternatively, we analyze the harmonic approximation to the correlator $U(ϕ)$ in a consistent manner. Using direct averaging as well as the replica technique, we derive the distribution functions ${\cal P}_{L,y}(F)$ and ${\cal P}_L(F)$ of free energies $F$ of a polymer of length $L$ for both fixed ($ϕ(L) = y$) and free boundary conditions on the displacement field $ϕ(x)$ and determine the mean displacement correlators on the distance $L$. The inconsistencies encountered in the analysis of the harmonic approximation to the correlator are traced back to its non-spectral correlator; we discuss how to implement this approximation in a proper way and present a general criterion for physically admissible disorder correlators $U(ϕ)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
