Le Doussal Pierre, Wiese Kay Jörg
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):035101. doi: 10.1103/PhysRevE.72.035101. Epub 2005 Sep 15.
We study elastic manifolds in an N -dimensional random potential using a functional renormalization group. We extend to N>1 our previous construction of a field theory renormalizable to two loops. For isotropic disorder with O (N) symmetry we obtain the fixed point and roughness exponent to next order in epsilon=4-d , where d is the internal dimension of the manifold. Extrapolation to the directed polymer limit d=1 allows some handle on the strong coupling phase of the equivalent N -dimensional Kardar-Parisi-Zhang growth equation, and eventually suggests an upper critical dimension d(u) approximately 2.5.
我们使用泛函重整化群研究了N维随机势中的弹性流形。我们将之前构建的可重整化至两圈的场论扩展到了N>1的情形。对于具有O(N)对称性的各向同性无序，我们得到了不动点和粗糙度指数，精确到ε=4 - d的下一阶，其中d是流形的内禀维度。外推到定向聚合物极限d = 1，使得我们能够对等效的N维Kardar-Parisi-Zhang增长方程的强耦合相有所了解，并最终给出一个大约为2.5的上临界维度d(u)。
