The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
复制标题
稀疏随机图上的随机场 XY 模型显示复制对称性破缺和边缘稳定的铁磁性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
F. Ricci
中科院分区：
文献类型：
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作者：
Cosimo Lupo;G. Parisi;F. Ricci
利用置信传播算法分析了随机场中稀疏随机图上的铁磁XY模型。在差异与完全连接的情况下，并与随机场伊辛模型在相同的拓扑结构，我们发现了强有力的证据，一个微小的区域与副本对称性破缺（RSB）的限制非常低的温度。该RSB相位对于外场方向的不同选择是鲁棒的，而当增加图形平均度、温度或外场中的方向偏置时，该RSB相位迅速消失。有这样一个RSB阶段的关键成分似乎是矢量自旋的连续性，主要是由不变的随机场，和强大的空间异质性，由于图稀疏。我们还发现，铁磁相可以是边缘稳定的，尽管存在的随机场。最后，我们研究适当的相关函数接近临界点，以确定那些变得更加关键。
The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find strong evidence of a tiny region with replica symmetry breaking (RSB) in the limit of very low temperatures. This RSB phase is robust against different choices of the external field direction, while it rapidly vanishes when increasing the graph mean degree, the temperature or the directional bias in the external field. The crucial ingredients to have such a RSB phase seem to be the continuous nature of vector spins, mostly preserved by the -invariant random field, and the strong spatial heterogeneity, due to graph sparsity. We also uncover that the ferromagnetic phase can be marginally stable despite the presence of the random field. Finally, we study the proper correlation functions approaching the critical points to identify the ones that become more critical.