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arXiv · 0807.3513

Ultrametricity and clustering of states in spin glasses: A one-dimensional view

Helmut G. Katzgraber·Alexander K. Hartmann
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Abstract

We present results from Monte Carlo simulations to test for ultrametricity and clustering properties in spin-glass models. By using 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 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.

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Helmut G. Katzgraber, Alexander K. Hartmann. 2009-01-26. Ultrametricity and clustering of states in spin glasses: A one-dimensional view. https://doi.org/10.1103/physrevlett.102.037207

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