Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.

DY 41.42: Poster

Thursday, April 3, 2014, 17:00–19:00, P3

Information-theoretic analysis of ground-state phase transitions for 2D and 3D frustrated spin systems — •Oliver Melchert and Alexander K. Hartmann — Universität Oldenburg

We consider standard information-theoretic observables [1] to analyze ground-state spin configurations for disordered and frustrated model systems. More precisely, we address the 2D random bond Ising model and the 3D random field Ising ferromagnet, which both exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied [2]. The ground-state configurations for both setups can be obtained in polynomial time via exact combinatorial optimization algorithms.

By computing the three observables entropy, i.e. a measure of disorder, excess entropy and multi-information, i.e. measures of complexity, it is possible to detect changes in the spatial structure of the ground states as the respective critical point is approached. The finite-size scaling behavior of the information-theoretic observables in the vicinity of the critical points is shown to be in excellent agreement with existing results on critical properties reported in the literature. Finally, we characterize the results of both ground-state phase transitions in the entropy-complexity plane, i.e. in purely information-theoretic coordinates.
 J.P. Crutchfield and D.P. Feldman, CHAOS 13 (2003) 25
 OM and A.K. Hartmann, Phys. Rev. E 87 (2013) 022107