We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. However, we encounter dramatic fluctuations in the behaviour of the model: averages over all the data only describe the behaviour of a small fraction of the data. 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 some of the measurements behave as the average, while the majority show 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. © 2014 IOP Publishing Ltd and SISSA Medialab srl.
Baity-Jesi, M., Banos, R.A., Cruz, A., Fernandez, L.A., Gil-Narvion, J.M., Gordillo-Guerrero, A., et al. (2014). The three-dimensional Ising spin glass in an external magnetic field: The role of the silent majority. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2014(5) [10.1088/1742-5468/2014/05/p05014].
The three-dimensional Ising spin glass in an external magnetic field: The role of the silent majority
Andrea Maiorano;
2014-01-01
Abstract
We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. However, we encounter dramatic fluctuations in the behaviour of the model: averages over all the data only describe the behaviour of a small fraction of the data. 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 some of the measurements behave as the average, while the majority show 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. © 2014 IOP Publishing Ltd and SISSA Medialab srl.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1126646