Helmut Katzgraber (Department of Physics & Astronomy, Texas A&M University and ETH Zurich)
Abstract. Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, despite ongoing research spanning several decades in the area of glassy systems, there remain many fundamental open questions. Rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range systems. Therefore large-scale numerical simulations are the tool of choice. Concepts from the solution of the mean-field model, such as ergodicity breaking, aging and ultrametricity have been applied to realistic short-range spin-glass models as well as to fields as diverse as structural biology, geology, computer science and even financial analysis. We study the critical behavior of Ising spin glasses—i.e., Boolean decision problems with competing interactions—on scale-free networks using large-scale Monte Carlo simulations and compare to analytical results. Our results show that these systems are remarkably stable to thermal (local) perturbations.
Work done in collaboration with C. K. Thomas and K. Janzen.