Ultrametricity and Clustering of States in Spin Glasses: A One-Dimensional View Academic Article uri icon


  • 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.

author list (cited authors)

  • Katzgraber, H. G., & Hartmann, A. K.

citation count

  • 13

publication date

  • January 2009