A Coarse graining for the Fortuin-Kasteleyn measure in random media
نویسنده
چکیده
Abstract. By the mean of a multi-scale analysis we describe the typical geometrical structure of the clusters under the FK measure in random media. Our result holds in any dimension d > 2 provided that slab percolation occurs under the annealed measure, which should be the case in the whole supercritical phase. This work extends the one of Pisztora [29] and provides an essential tool for the analysis of the supercritical regime in disordered FK models and in the corresponding disordered Ising and Potts models.
منابع مشابه
Nuclear Physics B235 [FSll] (1984) 19-23 © North-Holland Pubhshing Company THE CORRECT EXTENSION OF THE FORTUIN-KASTELEYN RESULT TO PLAQUE'I~E PERCOLATION
The work of Fortuin and Kasteleyn [1] demonstrated that bond percolation may be viewed as the s ~ 1 limit of the s-state Potts model. Recent interest in theories of random surfaces, particularly in the context of gauge theories [2], has led to the question of whether there is a natural generalization of the Fortuin-Kasteleyn result to plaquette percolation. It has been asserted that the proper ...
متن کاملRandom Cluster Model at Β > 1
We consider the Fortuin-Kasteleyn random cluster model on Z, with edge occupation probabilities p{x,y} = { p if |x− y| = 1, 1− exp { −β/ |x− y| } otherwise, and weighting factor κ ≥ 1. We prove that oriented percolation occurs when β > 1 and κ ≥ 1 provided p is chosen sufficiently close to 1. In the particular case of the product measure (κ = 1), this answers a question posed in [NS]. The proof...
متن کاملPercolation and Magnetization in the Continuous Spin Ising Model
In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding cluster distribution are analyzed. It is ...
متن کاملCritical exponents for the homology of Fortuin-Kasteleyn clusters on a torus.
A Fortuin-Kasteleyn cluster on a torus is said to be of type {a,b},a,b in Z , if it is possible to draw a curve belonging to the cluster that winds a times around the first cycle of the torus as it winds -b times around the second. Even though the Q -Potts models make sense only for Q integers, they can be included into a family of models parametrized by beta = square root of Q for which the Fo...
متن کاملPercolation and the Potts Model
The percolation process provides a simple picture of a critical point transition and has been of increasing recent theoretical interest. We refer to several review articles (1-a~ for a general survey of the subject. An important development first established by Kasteleyn and Fortuin (4,5~ is the connection between bond percolation and a lattice statistical model. This consideration leads to a f...
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 2007