Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Phase transitions and Critical Phenomena II

DY 28.2: Talk

Thursday, March 25, 2010, 14:30–14:45, H47

Ultrametricity and hierarchical clustering for Ising spin glasses — •Alexander K. Hartmann¹ and Helmut G. Katzgraber² — ¹Institut of Physics, University of Oldenburg, Germany — ²Department of Physics & Astronomy, Texas A&M University, USA

We present results from computer simulations [1], in particular Monte Carlo simulations using the parallel tempering approach, to test for ultrametricity [2] and clustering properties [3] in spin-glass models. We use a one-dimensional Ising spin glass with random power-law interactions where the universality class of the model can be tuned by changing the power-law exponent. We find [4] signatures of ultrametric behavior both in the mean-field and non-mean-field universality classes for large linear system sizes. Furthermore, we confirm the existence of nontrivial connected components in phase space via a clustering analysis of configurations.

[1] A.K. Hartmann, Practical Guide to Computer Simulations, (World Scientific, 2009)

[2] R. Rammal et al., Rev. Mod. Phys. 58, 765 (1986)

[3] G. Hed, A.K. Hartmann, D. Stauffer, and E. Domany, Phys. Rev. Lett. 86, 3148 (2001)

[4] H.G. Katzgraber and A.K. Hartmann, Phys. Rev. Lett. 102, 037207 (2009)