Stenull Olaf
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(1 Pt 2):015101. doi: 10.1103/PhysRevE.70.015101. Epub 2004 Jul 9.
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.
我们研究了一类广泛的无序系统中的多重分形特性，这类系统包括，例如，稀释的x-y模型。我们使用重整化场论分析了在渗流阈值处累积量平均动力学变量（对于x-y模型，是指定自旋方向的角度）的标度行为。每个累积量都有其独立的临界指数，也就是说，该问题涉及无限多个临界指数。通过研究与随机电阻网络的联系，我们将这些多重分形指数确定到两圈阶。根据每个具体模型哈密顿量的细节，高阶累积量的幅度可能会消失，在这种情况下，实际上只需要一些多重分形指数。
