title: 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.
authors.affiliation: Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland.
authors.forename: Helmut G
authors.initials: HG
authors.lastname: Katzgraber
authors.forename: Alexander K
authors.initials: AK
authors.lastname: Hartmann