Geometrical properties of parafermionic spin models

Abstract

We present measurements of the fractal dimensions associated to the geometrical clusters for Z_4 and Z_5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behaviour of these non local objects compared to the Ising model or the 3-state Potts model which corresponds to the simplest cases of Z_N spin models with N=2 and N=3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.

18 pages, 10 figures. v2: published version

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Cited by in corpus (10)

• Topics in coarsening phenomena
• Geometrical properties of Potts model during the coarsening regime
• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• Critical amplitude ratios of the Baxter-Wu model
• Critical interfaces and duality in the Ashkin Teller model
• A morphological study of cluster dynamics between critical points
• Critical interfaces of the Ashkin-Teller model at the parafermionic point
• Spin clusters and conformal field theory
• Conformal Curves in Potts Model: Numerical Calculation
• Spin interfaces and crossing probabilities of spin clusters in parafermionic models