Berlin 2012 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Phase Transitions and Critical Phenomena

DY 31.4: Vortrag

Freitag, 30. März 2012, 10:30–10:45, MA 004

The two-dimensional Ising spin glass at zero temperature — •Hamid Khoshbakht¹, Martin Weigel^1,2, and Jacob D. Stevenson³ — ¹Institut für Physik, Johannes Gutenberg-Universitaät Mainz, D-55099 Minz, Germany — ²Applied Mathematics Research Center, Coventry University, Coventry, CV1 5FB, UK — ³University Chemical Laboratories, Lensfield Road, Cambridge, CB2 1EW, UK

Ground states for the Ising spin glass in two dimensions can be determined in polynomial time as long as periodic boundary conditions are applied at most in 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. By using these techniques, we arrive at high-precision estimates of the spin-stiffness exponent and the domain-wall fractal dimension for Gaussian as well as bimodal couplings. We compare the geometry of the thus generated domain walls with the detailed predictions given for random curves in the plane in the framework of Schramm-Loewner Evolution (SLE).