Sharpness of the phase transition in percolation models
نویسندگان
چکیده
منابع مشابه
Approximate Zero-one Laws and Sharpness of the Percolation Transition in a Class of Models including Two-dimensional Ising Percolation
One of the most well-known classical results for site percolation on the square lattice is the equation pc + p ∗ c = 1. In words, this equation means that for all values 6= pc of the parameter p, the following holds: either a.s. there is an infinite open cluster or a.s. there is an infinite closed “star” cluster. This result is closely related to the percolation transition being sharp: below pc...
متن کاملApproximate zero-one laws and sharpness of the percolation transition in a class of models including 2D Ising percolation
One of the most well-known classical results for site percolation on the square lattice is the equation pc + p ∗ c = 1. In words, this equation means that for all values 6= pc of the parameter p the following holds: Either a.s. there is an infinite open cluster or a.s. there is an infinite closed ‘star’ cluster. This result is closely related to the percolation transition being sharp: Below pc ...
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If a system consists of a very small number of particles, we can attempt to predict its properties in complete detail using classical or quantum mechanics. If the system consists of a very large number of particles, we may only be able to predict average properties of the system in an approximate way. Statistical mechanics provides a formalism for predicting the average properties of systems, e...
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We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction ...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1987
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf01212322