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Ising模型是一种应用广泛的磁自旋相互作用模型,其二维情况严格求解极为复杂,实际应用中通常利用Wolff算法进行模拟.Wolff算法目前被认为是最好的聚类翻转Monte-Carlo算法.Metropolis和Swendsen-Wang算法同Wolff算法类似,理论上也适用于Ising模型的模拟,却未有文章将三者系统对比来说明Wolff算法的优越性,本科课程对于Monte-Carlo算法的介绍也较少.本文分别利用三种算法模拟了二维Ising模型,介绍了其算法原理、参数选择及实现方式,分析对比了三种算法的模拟效果和适用范围,从而总结说明在二维Ising模型的模拟中Wolff算法效果更好的原因. 相似文献
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李生好 《原子与分子物理学报》2016,33(6)
二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态 (iPEPS) 算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变. 相似文献
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二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态算法(iPEPS),在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还开创性提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变. 相似文献
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二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态(i PEPS)算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于i PEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变. 相似文献
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用Monte Carlo方法模拟了三维动态Ising模型中的非平衡相变,用统计的观点研究了序参量的大小和分布以描述该相变过程.保持温度和外场频率不变,改变外场大小使之由小到大变化,序参量由非零值变成零值.在低温阶段,序参量呈非连续变化,为典型的非连续相变,在高温阶段,序参量呈连续变化,为典型的连续相变.本文确定了界定非平衡转变的相界,并进一步确定了相界上区分非连续连续相变的三临界点.外场频率ω减小时,三临界点温度TTCP向高温部分移动,并满足TTCP=1.33×
关键词:
动态相变
Ising模型
三临界点 相似文献
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Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. 相似文献
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Computer simulation of phase transitions is made by the Monte Carlo method using a three-dimensional disordered antiferromagnetic Ising model in the external magnetic field. It is found that in the case where the spin concentration in a system is lower than a threshold one, the effects of random magnetic fields destroy the second-order phase transition and lead to the first-order phase transition into a new phase state of the system characterized by a ground spin-glassy state and metastable energy states at finite temperatures. The dependence of the threshold concentration on the external magnetic field is revealed. 相似文献
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E. V. Sannikov R. A. Kozlitin V. N. Udodov A. I. Potekaev 《Russian Physics Journal》2006,49(3):293-298
Ferromagnetic ↔ antiferromagnetic phase transitions for one-dimensional systems are investigated using the Monte Carlo technique.
Ground state diagrams are constructed within the framework of the Ising model. Using the Metropolis algorithm, the effects
of external magnetic field and temperature variations on phase transitions are examined. Kinetic features of these transitions
are included into consideration. It is shown that the correlational length coefficient v for ferromagnetic materials decreases
with increase in the external magnetic field strength, while for antiferromagnetic this dependence is reverse. Behavior of
the critical dynamic coefficient z under field variations for small one-dimensional magnetic is similar to that of coefficient
v.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp.54–58, March, 2006. 相似文献
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《Nuclear Physics B》1988,295(1):21-35
The first order phase transitions in the two-dimensional 10-state Potts model and in the two-dimensional Ising model with magnetic field are studied with Monte Carlo renormalization group methods. The deconfining phase transition of the four-dimensional U(1) lattice gauge theory is treated similarly. The results are not consistent with the standard discontinuity fixed point picture of first order phase transitions. In the U(1) case, where this possibility exists, they are not consistent with a second order phase transition either. The results show a discontinuous flow on the first order transition surface, which is a Monte Carlo renormalization group signal of singular RG transformations. 相似文献
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A. K. Murtazaev M. K. Ramazanov F. A. Kassan-Ogly M. K. Badiev 《Journal of Experimental and Theoretical Physics》2013,117(6):1091-1096
The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study. 相似文献
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We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence. 相似文献
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Magnetic properties of La_2CuMnO_6 double perovskite ceramic investigated by Monte Carlo simulations
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《中国物理 B》2020,(5)
We present a theoretical study of the magnetic properties of the lanthanum copper manganate double perovskite La_2CuMnO_6 ceramic, using Monte Carlo simulations. We analyze and discuss the ground state phase diagrams in different planes to show the effect of every physical parameter. Based on the Monte Carlo simulations, which combine Metropolis algorithm and Ising model, we explore the thermal behavior of the total magnetization and susceptibility. We also present and discuss the influence of physical parameters such as the external magnetic field, the exchange coupling interactions between magnetic atoms, and the exchange magnetic field on the magnetization of the system. Moreover, the critical temperature of the system is about T_c=70 K, in agreement with the experimental value. Finally, the hysteresis loops of La_2CuMnO_6 are discussed. 相似文献
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A Monte Carlo method for mapping a field theoretical or statistical system to a new theory embedded in a space-time of lesser dimensionality is presented. Typically, the critical properties of the dimensionally reduced system depend upon the details of the mapping. As an example, the two-dimensional Ising model is mapped to a one-dimensional Ising model with long-range forces and a phase transition. Systems with long-range interactions and known exponents can thus be constructed with this procedure. 相似文献
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Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks. 相似文献
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Stochastic evolutionary public goods game with first and second order costly punishments in finite populations
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We study the stochastic evolutionary public goods game with punishment in a finite size population. Two kinds of costly punishments are considered, i.e., first-order punishment in which only the defectors are punished, and second-order punishment in which both the defectors and the cooperators who do not punish the defective behaviors are punished. We focus on the stochastic stable equilibrium of the system. In the population, the evolutionary process of strategies is described as a finite state Markov process. The evolutionary equilibrium of the system and its stochastic stability are analyzed by the limit distribution of the Markov process. By numerical experiments, our findings are as follows.(i) The first-order costly punishment can change the evolutionary dynamics and equilibrium of the public goods game, and it can promote cooperation only when both the intensity of punishment and the return on investment parameters are large enough.(ii)Under the first-order punishment, the further imposition of the second-order punishment cannot change the evolutionary dynamics of the system dramatically, but can only change the probability of the system to select the equilibrium points in the "C+P" states, which refer to the co-existence states of cooperation and punishment. The second-order punishment has limited roles in promoting cooperation, except for some critical combinations of parameters.(iii) When the system chooses"C+P" states with probability one, the increase of the punishment probability under second-order punishment will further increase the proportion of the "P" strategy in the "C+P" states. 相似文献