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

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.

4 pages, 4 figures, 1 table

References in corpus (5)

• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Ultrametricity in the Edwards-Anderson Model
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Comment on "Ultrametricity in the Edwards-Anderson Model"

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• Hamming Distance and the onset of quantum criticality
• A multimode cavity QED Ising spin glass
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