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.

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

MANTOVANI, Filippo;PIVANTI, Marcello;SCHIFANO, Sebastiano Fabio;TRIPICCIONE, Raffaele;
2014

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
M., Baity Jesi; R. A., Baños; A., Cruz; L. A., Fernandez; J. M., Gil Narvion; A., Gordillo Guerrero; D., Iñiguez; A., Maiorano; Mantovani, Filippo; E....espandi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2082812
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