The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius
نویسنده
چکیده
We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar’s solution obtained originally for a directed polymer with δ-correlated random potential can be applied for the description of the present system only in the high-temperature limit. For the low temperature limit we have obtained the new solution which is described by the one-step replica symmetry breaking. For the mean square deviation of the directed polymer of the linear size L it provides the usual scaling x ∼ aL2ζ with the wandering exponent ζ = 2/3 and the temperature-independent prefactor.
منابع مشابه
Some new results on Brownian Directed Polymers in Random Environment
We prove some new results on Brownian directed polymers in random environment recently introduced by the authors. The directed polymer in this model is a d-dimensional Brownian motion (up to finite time t) viewed under a Gibbs measure which is built up with a Poisson random measure on R+×R (=time × space). Here, the Poisson random measure plays the role of the random environment which is indepe...
متن کاملTesting a Variational Approach to Random Directed Polymers
The one dimensional direct polymer in random media model is investigated using a variational approach in the replica space. We demonstrate numerically that the stable point is a maximum and the corresponding statistical properties are for the delta correlated potential in good agreements with the known analytic solution. In the case of power-law correlated potential two regimes are recovered: a...
متن کاملOn the Thermal Conductivity of Carbon Nanotube/Polypropylene Nanocomposites by Finite Element Method
In this paper, finite element method is used to obtain thermal conductivity coefficients of single-walled carbon nanotube reinforced polypropylene. For this purpose, the two-dimensional representative volume elements are modeled. The effect of different parameters such as nanotube dispersion pattern, nanotube volume percentage in polymer matrix, interphase thickness between nanotube and surroun...
متن کاملSelf-Avoiding Walks with Writhe
We map self-avoiding random walks with a chemical potential for writhe to the three-dimensional complex O(N) Chern-Simons theory as N → 0. We argue that at the Wilson-Fisher fixed point which characterizes normal selfavoiding walks (with radius of gyration exponent ν ≈ 0.588) a small chemical potential for writhe is irrelevant and the Chern-Simons field does not modify the monomer-monomer corre...
متن کاملThe Largest Liapunov Exponent for Random Matrices and Directed Polymers in a Random Environment
We study the largest Liapunov exponent for products of random matrices. The two classes of matrices considered are discrete, d-dimensional Laplacians, with random entries, and symplectic matrices that arise in the study of d-dimensional lattices of coupled, nonlinear oscillators. We derive bounds on this exponent for all dimensions, d, and we show that if d 3, and the randomness is not too stro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008