恭喜MDPI期刊Entropy作者——意大利罗马大学物理学家Giorgio Parisi，与美国普林斯顿大学的日裔气象学家Syukuro Manabe，德国马克斯-普朗克研究院汉堡气象学研究所学者Klaus Hasselmann荣获2021年诺贝尔物理学奖。Giorgio Parisi 因“发现了从原子到行星尺度的物理系统中无序和波动的相互作用”荣获诺贝尔物理学奖，对此我们表示衷心的祝贺！

 

 

文章引读

 

Spin Glasses in a Field Show a Phase Transition Varying the Distance among Real Replicas (And How to Exploit It to Find the Critical Line in a Field)

Giorgio Parisi et al.

https://doi.org/10.3390/e22020250

We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h>0 and Tc(h)<T<Tc(h=0) , of the d=1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field.