Fractal Structure of Ising and Potts Clusters: Static and Dynamic Approach View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1989

AUTHORS

Antonio Coniglio

ABSTRACT

How to characterize geometrically a fluctuation near a critical point is a longstanding problem1−8 that recently has received renewed attention, due to a novel experiment in which direct visual observation of critical fluctuations was possible9. Here I want to describe a static and dynamic approach to this problem. The static approach is based on a particular site bond correlated percolation model which was previously introduced as a model for sol gel transition10, For a particular value of the bond probability4, this approach can be related to a formalism developped by Kasteleyn and Fortuin3,11 and gives the correct definition of the Ising and Potts clusters for a geometrical description of the phase transition. I will first review the main results and show how the formalism can be extended to the case of non zero magnetic field. In Sect. III–V I will present exact results12 on the fractal structure of the Ising and Potts clusters based on a mapping13 from the Potts model to the Coulomb gas. In Sec. VI it will be shown that a model originally introduced by Mandelbrot and Given14 for percolation clusters is found extremely good to describe the fractal structure of the Potts clusters. Finally Sec. VII is devoted to a dynamical approach which has been recently15 introduced and is based on the propagation of “damage” in a spin system. More... »

PAGES

123-133

References to SciGraph publications

Book

TITLE

Fractals’ Physical Origin and Properties

ISBN

978-1-4899-3501-4
978-1-4899-3499-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4899-3499-4_5

DOI

http://dx.doi.org/10.1007/978-1-4899-3499-4_5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1041990670


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