蒙特卡罗方法研究层状含集团权重伊辛模型相变  

Phase Transitions in Layered Ising Model with Cluster Weight by Monte Carlo Method

作　　者：王孜阳 丁成祥 张万舟 WANG Ziyang;DING Chengxiang;ZHANG Wanzhou(School of Physics and Optoelectronic Engineering,Taiyuan University of Technology,Taiyuan 030006,China;School of Science and Engineering of Mathematics and Physics,Anhui University of Technology,Ma'anshan 243000,China;CAS Key Laboratory of Quantum Information,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]太原理工大学物理与光电工程学院,山西太原030006 [2]安徽工业大学数理科学与工程学院,安徽马鞍山243000 [3]中国科学技术大学、中国科学院量子信息重点实验室,安徽合肥230026

出　　处：《山西大学学报（自然科学版）》2023年第2期381-389,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：中科院量子信息重点实验室开放课题(KQI201)。

摘　　要：三维Ising模型是统计力学中的一个非常重要的模型,在描述三维Ising模型的配分函数中引入集团权重因子n可以得到新的临界指数和普适类,但人们尚不清楚集团权重因子对其他晶格结构中的Ising模型的影响。本文尝试研究另外一种几何结构,层状含集团权重Ising模型,通过将着色算法和Swendsen-Wang算法相结合给出高效的集团演化方法,计算出的磁化强度m、磁化率χ、比热Cv和宾德累积量Q,并拟合出临界指数y_(t)和y_(m)以及其它指数α,β,γ,δη,υ。由于拓扑结构不同,尽管双层模型在n=1.5时也是一级相变,但临界指数与三维模型有所差别,表明两者属于不同的普适类。n=3时,能量直方图的双峰结构和磁滞回线表明双层模型发生一级相变,和三维晶格的结论一致。此外,本文发现了之前工作尚未注意到的现象,n≥3时,系统发生的是铁磁到反铁磁之间的几何相变。本文的结果对于理解统计力学自旋模型有一定的促进作用。The three-dimensional Ising model is a very important model in statistical mechanics,and new critical exponents and universalities can be obtained by introducing the cluster weight factor n into the partition function describing the three-dimensional Ising model.However,it is not clear how the cluster weight factor affects the Ising model on the lattices with other types of structures.In this paper,we try another geometric structure and study the layered Ising model with cluster weight,and give an efficient cluster-update method by combining the coloring method and the Swendsen-Wang algorithm.The the magnetization m,susceptibilityχ,specific heat Cvand Binder accumulation Q,and the thermal critical exponent y_(t)and y_(m)as well as other critical exponentsα,β,γ,δ,η,υare calculated.When n=1.5,although the layered model undergoes a continuous phase transition,the critical exponent yt of the two models are different,indicating that the two models belong to different universalities due to the different topology.At n=3,the bimodal structure of the energy histogram and the hysteresis of energy indicate that the bilayer cluster weight Ising model belongs to the first-order phase transition which is consistent with the type of phase transition in the three-dimensional lattice.In addition,this paper identifies a phenomenon that the system undergoes a geometric phase transition from a ferromagnet to an antiferromagnet at n≥3 which has not been noticed in previous work.The results of this paper are useful for understanding spin models statistical mechanics.

关 键 词：集团权重伊辛模型 相变 临界指数 Swendsen-Wang算法 

分 类 号：O436[机械工程—光学工程]