Non-Self Averaging in Autocorrelations for Potts Models on Quenched Random Gravity Graphs

Abstract

We investigate the non-self-averaging properties of the dynamics of Ising, 4-state Potts and 10-state Potts models in single-cluster Monte Carlo simulations on quenched ensembles of planar, trivalent Phi3 random graphs, which we use as an example of relevant quenched connectivity disorder. We employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetisation in order to discern non-self-averaging. Although the specific results discussed here are for quenched random graphs, the method has quite general applicability.

9 pages + 11 figures

References in corpus (4)

• Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
• Quenched Randomness at First-Order Transitions
• Critical Exponents near a Random Fractal Boundary
• The Wrong Kind of Gravity

Cited by in corpus (7)

• The Harris-Luck criterion for random lattices
• Ising model on 3D random lattices: A Monte Carlo study
• Frustration effects in antiferromagnets on planar random graphs
• Ising and Potts Models on Quenched Random Gravity Graphs
• Self-averaging in the random 2D Ising ferromagnet
• Dynamical Critical Properties of the Random-Bond three-state Potts Model
• Harris-Luck criterion in the plateau transition of the Integer Quantum Hall Effect