Critical domain walls in the Ashkin-Teller model

Abstract

We study the fractal properties of interfaces in the 2d Ashkin-Teller model. The fractal dimension of the symmetric interfaces is calculated along the critical line of the model in the interval between the Ising and the four-states Potts models. Using Schramm's formula for crossing probabilities we show that such interfaces can not be related to the simple SLE${}_{\kappa }$, except for the Ising point. The same calculation on non-symmetric interfaces is performed at the four-states Potts model: the fractal dimension is compatible with the result coming from Schramm's formula, and we expect a simple SLE${}_{\kappa }$ in this case.

Final version published in JSTAT. 13 pages, 5 figures. Substantial changes in the data production, analysis and in the conclusions. Added a section about the crossing probability. Typeset with 'iopart'

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Cited by in corpus (4)

• Phase separation and interface structure in two dimensions from field theory
• Critical interfaces and duality in the Ashkin Teller model
• Schramm-Loewner evolution in 2d rigidity percolation
• Spin interfaces in the Ashkin-Teller model and SLE