On the origin of ultrametricity

Abstract

In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural assumptions: each replica is equivalent to the others (replica equivalence or stochastic stability) and all the mutual information about a pair of equilibrium configurations is encoded in their mutual distance or overlap (separability or overlap equivalence).

13 pages, 1 figure

References in corpus (4)

• Measuring equilibrium properties in aging systems
• About the overlap distribution in mean field spin glass models
• On the Dynamics of the 4d Spin Glass in a magnetic field
• Are Ground States of 3d +/-J Spin Glasses ultrametric ?

Cited by in corpus (21)

• Critical Behavior of the Three-Dimensional Ising Spin Glass
• An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Nature of the spin-glass phase at experimental length scales
• Temperature chaos in 3D Ising Spin Glasses is driven by rare events
• Ultrametricity in the Edwards-Anderson Model
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Overlap Equivalence in the Edwards-Anderson Model
• Against Chaos in Temperature in Mean-Field Spin-Glass Models
• Replica equivalence in the Edwards-Anderson model
• Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass
• Some considerations of finite dimensional spin glasses
• The marginally stable Bethe lattice spin glass revisited
• The cumulative overlap distribution function in realistic spin glasses
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Cluster formation in complex multi-scale systems
• Spin-glass dynamics: experiment, theory and simulation
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Non-trivial link overlap distribution in three-dimensional Ising spin glasses
• Spatial correlation functions and dynamical exponents in very large samples of 4D spin glasses