Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 40: Posters II

DY 40.38: Poster

Thursday, March 17, 2011, 17:00–19:00, P3

The two-dimensional Ising spin glass at zero temperature — •Hamid Khoshbakht and Martin Weigel — Institut für Physik, KOMET 331, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55127 Mainz

Ground states for the Ising spin glass in two dimensions can be determined in polynomial time as long as periodic boundary conditions are applied in at most one direction. Using a recently proposed mapping to an auxiliary graph decorated with Kasteleyn cities, we determine ground states for systems with open-periodic boundary conditions for lattices of linear sizes up to L = 9000 and calculate defect energies as well as domain-wall lengths. Although the matching approach does not work for periodic-periodic boundaries, where less finite-size corrections are expected, using a windowing technique allows to determine quasi-exact ground-states for lattices up to L = 3000. For the case of bimodal couplings, a controlled perturbation method allows the matching approach to sample from the manifold of degenerate ground states without bias. Using the combination of these techniques, we arrive at high-precision estimates of the spin-stiffness exponent and domain-wall fractal dimension for Gaussian couplings, which are compared to a scaling relation conjectured from stochastic Loewner evolution. For bimodal couplings, our results allow for a first-time determination of the fractal dimension of domain walls.