Berlin 2018 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 18: Critical Phenomena and Phase Transitions
DY 18.2: Talk
Monday, March 12, 2018, 15:45–16:00, BH-N 333
The plain and layered Ising spin glasses in two dimensions — •Martin Weigel1, Hamid Khoshbakht1,2, Mohammad-Sadegh Vaezi3, Gerardo Ortiz4, and Zohar Nussinov3 — 1Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England — 2Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany — 3Department of Physics, Washington University, St. Louis, MO 63160, USA — 4Department of Physics, Indiana University, Bloomington, IN 47405, USA
The Ising spin glass in 2D exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use combinatorial optimization methods to determine exact ground states for systems with up to 10 000× 10 000 spins. A combination of new algorithms allow us to treat samples with fully periodic boundaries and to sample uniformly from degenerate ground states for the ± J model. To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the binomial spin glass. In this model, the couplings are the sum of m identically distributed Bernoulli random variables. In the continuum limit m → ∞, this system reduces to the Edwards-Anderson model with Gaussian couplings, while m=1 corresponds to the ± J spin glass. Using this model, we derive a rigorous bound for the degeneracy of any energy level. Studying the defect energies in this model, we uncover intriguing subtleties in the behavior of the model with respect to the order in which the thermodynamic (N→∞) and continuum (m→∞) limits are taken.