Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-08-04
Phys.Rev. E62 (2000) 3125-3134
Physics
High Energy Physics
High Energy Physics - Phenomenology
1 LaTeX file, 4 figures in ps-files. Accepted for publication in Physical Review E
Scientific paper
10.1103/PhysRevE.62.3125
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with fractal geometry, where the term cluster is used to describe regions with a nonvanishing value of the order parameter. We show that, treating the cluster as an open subsystem of the entire system, new instanton-like configurations dominate the statistical mechanics of the cluster. We study the dependence of the resulting fractal dimension on the embedding dimension and the scaling properties (isothermal critical exponent) of the system. Taking into account the finite size effects we are able to calculate the size of the critical cluster in terms of the total size of the system, the critical temperature and the effective coupling of the long wavelength interaction at the critical point. We also show that the size of the cluster has to be identified with the correlation length at criticality. Finally, within the framework of the mean field approximation, we extend our local considerations to obtain a global description of the system.
Antoniou N. G.
Contoyiannis Y. F.
Diakonos Fotios K.
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