Critical domain walls in the Ashkin-Teller model

Details Critical domain walls in the Ashkin-Teller model Critical domain walls in the Ashkin-Teller model

2009-07-29

arxiv.org/abs/0907.5094v3

J.Stat.Mech.1102:P02039,2011

Physics

Condensed Matter

Statistical Mechanics

Final version published in JSTAT. 13 pages, 5 figures. Substantial changes in the data production, analysis and in the conclus

Scientific paper

10.1088/1742-5468/2011/02/P02039

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.

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