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

Janus Collaboration, M. Baity-Jesi, R. A. Banos, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, D. Iniguez, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, M. Pivanti, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, S. F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, D. Yllanes

Published 2014-03-11, updated 2014-04-02Version 2

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.