The Universal Relation between Scaling Exponents in First-passage Percolation
نویسنده
چکیده
It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent χ and the wandering exponent ξ are related through the universal relation χ = 2ξ − 1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.
منابع مشابه
First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials
0022-4715/98/0500-0603$15.00/0 © 1998 Plenum Publishing Corporation We present a two-dimensional, quasistatic model of fracture in disordered brittle materials that contains elements of first-passage percolation, i.e., we use a minimum-energy-consumption criterion for the fracture path. The first-passage model is employed in conjunction with a "semi-directed" Bernoulli percolation model, for wh...
متن کاملTHE SCALING LAW FOR THE DISCRETE KINETIC GROWTH PERCOLATION MODEL
The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scal...
متن کاملPercolation properties of the Wolff clusters in planar triangular spin models.
We formulate the Wolff algorithm as a site-bond percolation problem, apply it to the ferromagnetic and antiferromagnetic planar triangular spin models, and study the percolation critical behavior using Anite-size scaling. In the former case the Wold' algorithm is successful as an accelerating algorithm, whereas in the latter case it is not. We found the percolation temperatures and the cluster ...
متن کاملConformal invariance and universal critical exponents in the two-dimensional percolation model
For most two-dimensional critical percolation models, we show the existence of a scaling limit for the crossing probabilities in an isosceles right triangle. Furthermore, by justifying the lattice, the scaling limit is a conformal invariance satisfying Cardy’s formula in Carleson’s form. Together with the standard results of the SLE6 process, we show that most critical exponents exist in the se...
متن کاملJa n 20 05 Universal scaling behavior of non - equilibrium phase transitions Sven Lübeck
Non-equilibrium critical phenomena have attracted a lot of research interest in the recent decades. Similar to equilibrium critical phenomena, the concept of universality remains the major tool to order the great variety of non-equilibrium phase transitions systematically. All systems belonging to a given universality class share the same set of critical exponents, and certain scaling functions...
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 2012