Conformal Curves in Potts Model: Numerical Calculation

Abstract

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE${}_{\kappa }$.

11 Pages, 4 figures

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Cited by in corpus (6)

• Efficient simulation of the random-cluster model
• Critical interfaces of the Ashkin-Teller model at the parafermionic point
• Theta-point polymers in the plane and Schramm-Loewner evolution
• Numerical study of Schramm-Loewner Evolution in the random 3-state Potts model
• Duality of critical interfaces in Potts model: numerical check
• q-deformed Loewner evolution