The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority

Abstract

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.

42 pages, 19 figures. Minor changes and added figure (results unchanged)

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Cited by in corpus (10)

• Absence of Marginal Stability in a Structural Glass
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Low-temperature anomalies of a vapor deposited glass
• From local to global ground states in Ising spin glasses
• The cumulative overlap distribution function in realistic spin glasses
• Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• 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)
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range
• Specific heat and non-linear susceptibility in spin glasses with random fields