Numerical construction of the Aizenman-Wehr metastate

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Numerical construction of the Aizenman-Wehr metastate

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Title: Numerical construction of the Aizenman-Wehr metastate
Author: Billoire, Alain; Fernández Pérez, Luis Antonio; Maiorano, Andrea; Marinari, Enzo; Martín Mayor, Víctor; Moreno Gordo, Javier; Parisi, Giorgio; Ricci Tersenghi, Federico; Ruiz Lorenzo, Juan Jesús
Abstract: La dependencia de tamaño caótico hace que sea extremadamente difícil tomar el límite termodinámico en sistemas desordenados. En cambio, el metastato, que es una distribución sobre los estados termodinámicos, podría tener un límite uniforme. Hasta ahora, los estudios sobre el metastato han sido principalmente matemáticos. Presentamos una construcción numérica del metastato para el vidrio de hilado d ¼ 3 Ising. Trabajamos en equilibrio, por debajo de la temperatura crítica. Aprovechando los resultados rigurosos recientes, nuestro análisis numérico da evidencia de un metastato disperso, apoyado en muchos estados termodinámicos.Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d ¼ 3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states.
URI: http://hdl.handle.net/10662/8985
Date: 2017


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