特殊结构下Potts模型的混沌重整化群映射轨迹研究
首发时间:2021-01-20
摘要:混沌的RG映射轨迹被认为是自旋玻璃态的标志。本文在钻石层级晶格上的Potts模型中以一定的规则加入长程关联作用,并对模型进行重整化群分析。在特定参数下,该系统会出现混沌重整化群(RG)映射轨迹。这说明系统在热力学极限下进入了自旋玻璃态。通过对该模型进行分析,发现本文中添加的长程关联作用起到了关键的"阻挫"作用。在能使RG映射轨迹达到混沌的系统参数下,复平面下的RG映射的Julia set 也将覆盖住实轴的部分区间。
关键词: 重整化群 Potts模型 长程关联作用 混沌轨迹 自旋玻璃态 Julia set
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Chaotic trajectory of RG map in Potts model with special structure
Abstract:The chaotic RG map trajectory is considered to be the sign of spin glass. In this paper, we add a long-range interaction to the Potts model on hierarchical diamond lattice with certain rules and analyze the renormalization group of the model. It is found that the chaotic renormalization group (RG) maptrajectories appears under certain parameters. This indicates that the system enters the spin glass state in the thermodynamic limit. Through the analysis of the model, it is found that the long-range interaction function added in this paper plays a key role of "frustration". The Julia set of the RG map in the complex plane will also cover part of the real axis under the parameters that can make the RG map trajectories chaotic.
Keywords: Renormalization group Potts model Long-rang interaction Chaotic trajectory Spin glass Julia set
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