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.
The three-dimensional Ising spin glass in an external magnetic field: The role of the silent majority / M., Baity Jesi; R. A., Banos; A., Cruz; L. A., Fernandez; J. M., Gil Narvion; A., Gordillo Guerrero; D., Iniguez; Maiorano, Andrea; F., Mantovani; Marinari, Vincenzo; V., Martin Mayor; J., Monforte Garcia; A., Munoz Sudupe; D., Navarro; Parisi, Giorgio; S., Perez Gaviro; M., Pivanti; RICCI TERSENGHI, Federico; J. J., Ruiz Lorenzo; S. F., Schifano; SEOANE BARTOLOME, Beatriz; A., Tarancon; R., Tripiccione; YLLANES MOSQUERA, David. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2014:5(2014), p. P05014. [10.1088/1742-5468/2014/05/p05014]
The three-dimensional Ising spin glass in an external magnetic field: The role of the silent majority
MAIORANO, Andrea;MARINARI, Vincenzo;PARISI, Giorgio;RICCI TERSENGHI, Federico;SEOANE BARTOLOME, BEATRIZ;YLLANES MOSQUERA, DAVID
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 IOP Publishing Ltd and SISSA Medialab srl.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.