Dresden 2014 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.
DY 41.46: Poster
Donnerstag, 3. April 2014, 17:00–19:00, P3
Critical Temperature of the Ising Ferromagnet on Proximity Graphs derived from Square Lattices by Site Displacement — •Hendrik Schawe, Christoph Norrenbrock, and Alexander K. Hartmann — Institut für Physik, Carl-von-Ossietzky Universität Oldenburg, Oldenburg (Germany)
We perform Monte Carlo simulations to determine the critical temperatures of an Ising Ferromagnet (IFM) located on the sites of different types of 2D proximity graphs. The graphs are derived from square lattices where nodes are displaced by a Gaussian distributed random variable. The deviation of the proximity graph from a square lattice is governed by the width σ of the Gaussian distribution. In our model, the coupling strength depends on the Euclidean distance between the coupled spins. The simulations are carried out on graphs with N=162 to N=1282 nodes utilizing the Wolff cluster algorithm and parallel tempering in a wide temperature range around the critical point to measure the Binder Cumulant. The critical temperatures are shown to depend mainly on the average degree and the type of the underlying proximity graph. We further verify that the model lies within the universality class of the 2D IFM using finite-size scaling methods.