Regensburg 2013 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 25: Critical Phenomena and Phase Transitions
DY 25.9: Talk
Thursday, March 14, 2013, 11:45–12:00, H46
Stochastic Loewner evolution in the 2D Ising spin glass depends on boundary conditions — •Hamid Khoshbakht1,2, Martin Weigel1,2, and Jacob D. Stevenson3 — 1Institut für Physik, Johannes Gutenberg-Universitaät Mainz, D-55099 Minz, Germany — 2Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK — 3University Chemical Laboratories, Lensfield Road, Cambridge, CB2 1EW, UK
Domain walls in two-dimensional Ising spin glasses are scale-invariant curves with fractal dimension df. Recent works indicate that df≈1.27 for Gaussian bond distribution and 1.09 ≲ df ≲ 1.39 for bimodal couplings. In this contribution, we investigate whether the domain wall of this system satisfies Schramm-Loewner evolution (SLE) and is therefore also conformally invariant. Different boundary conditions are considered, and for each case df and the SLE diffusion constant κ of the corresponding Brownian motion are calculated. Correlations between different domain-wall segments are explicitly checked for by testing for independence of the increments of the Loewner driving function. The results show that changing the boundary conditions of the system does not change the fractal dimension, but the stronger conditions of SLE are only satisfied for specific choices of boundary conditions. In this sense, SLE is not universal.