Monte Carlo study on bilayer thin films magnetic properties dependence with discontinouos anisotropy parameters

In the last few years there has been significant interest in the field of thin films, due to numerous specific phenomena related to the low dimension of these systems, and to the large opportunities in development of high technologies based on their specific magnetic and electronic properties. When dealing with systems of reduced dimensionality it is important to take into account the influence of magnetic anisotropies. In this paper we investigate the magnetic properties of bilayer thin film. This behavior is modeled using Monte Carlo simulations, in the Extended Anisotropic Heisenberg Model. The magnetization, out-of-plane and in-plane magnetic susceptibilities, and also the specific heat bearings according to temperature are investigated in order to find the potential magnetic ordering phases and the critical temperatures, for two sets parameter assignments. For quasi-uniform anisotropy parameters of the film we detect the ferromagnetism-paramagnetism transition and then, by changing the model parameters values, we relieve a short range ferromagnetic ordering phase arising from the antiferromagnetic base layer coupling influence and from easy-plane anisotropy discontinuity on the layers interface.      

R32热力学性质的蒙特卡罗模拟

建立在统计热力学和分子力学理论基础上的分子模拟方法逐渐运用于计算制冷剂的热力学性质。文中首先在NVT系综条件下,采用吉布斯蒙特卡罗模拟方法(GEMC),模拟了R32的气液相平衡的密度、饱和蒸汽压及蒸发焓;其次在NPT系综条件下,采用蒙特卡罗模拟方法(MC),模拟了R32在4MPa条件下的过冷液态密度。模拟结果同美国国家标准研究所(NIST)的Refprop 8.0相比,有很好的一致性。结果表明,运用该方法预测单一制冷剂的热力学性质是可行的。     

Thermodynamic properties of water in confined environments: a Monte Carlo study

Monte Carlo simulations of Mercedes-Benz water in a crowded environment were performed. The simulated systems are representative of both composite, porous or sintered materials and living cells with typical matrix packings. We studied the influence of overall temperature as well as the density and size of matrix particles on water density, particle distributions, hydrogen bond formation and thermodynamic quantities. Interestingly, temperature and space occupancy of matrix exhibit a similar effect on water properties following the competition between the kinetic and the potential energy of the system, whereby temperature increases the kinetic and matrix packing decreases the potential contribution. A novel thermodynamic decomposition approach was applied to gain insight into individual contributions of different types of inter-particle interactions. This decomposition proved to be useful and in good agreement with the total thermodynamic quantities especially at higher temperatures and matrix packings, where higher-order potential-energy mixing terms lose their importance.     

Monte Carlo calculation of the thermodynamic properties of a one-dimensional fermion lattice model

The generalized Trotter formula is used to derive two different classical representations of the partition function of a one-dimensional fermion model. Shortchain calculations are used to study the corresponding approximants for the energy and specific heat. A Monte Carlo technique has been used to calculate the temperature-dependent properties of a chain of 64 sites.     

磁性纳米颗粒系统偶极相互作用的Monte Carlo研究

采用局域Monte Carlo方法模拟不同易轴分布的简单立方排列单分散单畴Fe纳米颗粒系统的ZFC-FC曲线及磁滞回线.结果表明：随着偶极相互作用的增强，系统的阻塞温度T_B逐渐增大，且ZFC曲线的峰变宽.说明偶极相互作用使得系统的有效能垒提高，分布宽度增加.研究FC曲线磁化强度的倒数与温度关系，发现偶极相互作用系统中存在反铁磁有序.系统的阻塞态及超顺磁态的磁滞回线表明，极低低温下，随着偶极相互作用的增强，系统的矫顽力和剩磁减小，偶极相互作用阻碍系统的磁化；系统处于超顺磁态，各向异性作用及偶极相互作用使得系统的磁化曲线偏离Langevin曲线且偶极相互作用展现出退磁相互作用效应.偶极相互作用增强，系统磁化曲线与Langevin曲线偏差量的最大值向低场移动.在偶极相互作用下，易轴与外场夹角为45°的磁性纳米颗粒系统的平均有效能垒和有效能垒分布宽度较易轴随机分布系统的大.     

气泡幕后向散射光信号特性的蒙特卡罗方法研究

利用蒙特卡罗方法对水介质中的气泡幕的后向光散射回波信号进行了系统仿真。通过对计算结果与实验结果的比较,证明了蒙特卡罗方法的有效性。根据仿真结果,结合理论分析的方法,对气泡幕位置、厚度和接收器视场角等参数对回波信号的影响进行了分析,结果表明:回波信号出现时间与气泡幕位置存在一一对应的关系;在气泡幕的衰减系数ρσt不变的情况下,存在一个有效气泡幕厚度,当大于该厚度时,气泡幕的后向光散射回波信号基本不变;在系统各项参数不变的情况下,适当增加接收器的视场角,可有效地提高回波信号的信噪比。     

Monte Carlo study of nanowire magnetic properties

In this work, we use Monte Carlo simulations to study the magnetic properties of a nanowire system based on a honeycomb lattice, in the absence as well as in the presence of both an external magnetic field and crystal field. The system is formed with NL layers having spins that can take the values σ = ±1/2 and S = ±1, 0. The blocking temperature is deduced, for each spin configuration, depending on the crystal field Δ. The effect of the exchange interaction coupling Jp between the spin configurations σ and S is studied for different values of temperature at fixed crystal field. The established ground-state phase diagram, in the plane (Jp ,Δ), shows that the only stable configurations are: (1/2, 0), (1/2, +1), and (1/2,-1). The thermal magnetization and susceptibility are investigated for the two spin configurations, in the absence as well as in the presence of a crystal field. Finally, we establish the hysteresis cycle for different temperature values, showing that there is almost no remaining magnetization in the absence of the external magnetic field, and that the studied system exhibits a super-paramagnetic behavior.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

The effect of a surface on the dynamic and thermodynamic properties of S=1 Heisenberg ferromagnet with biquadratic exchange

Properties of semi-infinite (S=1) Heisenberg ferromagnet with biquadratic exchange were studied in terms of surface exchange (=I_S/I) and biquadratic coupling (a). It was shown that a strict correlation exists, depending on , between the type of surface spin waves (acoustic or optical) and the mean-field (MF) critical temperature, bulk (T_c) and surface T_c^S>T_c (for ). Within the framework of the Landau–Ginsburg theory for semi-infinite simple cubic ferromagnet, a detailed study is presented of the critical behaviour of the system, in particular in the vicinity of the tricritical point which is the consequence of the biquadratic interaction. It is shown that tricritical exponents satisfy exactly the scaling relations for d=3. The analysis of the spin–spin correlation function within the framework of the same theory, shows that there occurs the critical magnetic scattering of low-energy electrons (LEED) from the surface in the case , when the ordering temperature T_c^S is approached from above (from paramagnetic phase). In the opposite case, , there occurs no surface critical scattering. It was also shown that in the vicinity of the tricritical point, the biquadratic interaction increases the range of validity of the MF approximation.     

Worm Monte Carlo study of the honeycomb-lattice loop model

We present a Markov-chain Monte Carlo algorithm of worm   type that correctly simulates the O(n)$O(n)$ loop model on any (finite and connected) bipartite cubic graph, for any real n>0$n>0$, and any edge weight, including the fully-packed limit of infinite edge weight. Furthermore, we prove rigorously that the algorithm is ergodic and has the correct stationary distribution. We emphasize that by using known exact mappings when n=2$n=2$, this algorithm can be used to simulate a number of zero-temperature Potts antiferromagnets for which the Wang–Swendsen–Kotecký cluster algorithm is non-ergodic, including the 3-state model on the kagome lattice and the 4-state model on the triangular lattice. We then use this worm algorithm to perform a systematic study of the honeycomb-lattice loop model as a function of n?2$n?2$, on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify a set of exact expressions for scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n?2$n?2$, the scaling of a certain return time in the worm dynamics is governed by the magnetic dimension of the loop model, thus providing a concrete dynamical interpretation of this exponent. The case n>2$n>2$ is also considered, and we confirm the existence of a phase transition in the 3-state Potts universality class that was recently observed via numerical transfer matrix calculations.     

Monte Carlo study of self-avoiding surfaces

Two models of self-avoiding surfaces on the cubic lattice are studied by Monte Carlo simulations. Both the first model with fluctuating boundary and the second one with a fixed boundary are found to belong to the universality class of branched polymers. The algorithms as well as the methods used to extract the critical exponents are described in detail. The results are compared to other recent estimates in the literature.     

Monte Carlo investigation of the correlation between magnetic and chemical ordering in NiFe alloys

The Ni_xFe_1−x alloys close to the stoichiometric Ni₃Fe composition are modeled by means of Monte Carlo simulations. To describe the atomic and magnetic configurations, the Ising and Heisenberg models with nearest-neighbor interactions have been used, respectively. The pairwise interactions have been fitted to the experimentally measured Curie and Kurnakov temperatures, the Fe-Fe magnetic exchange interaction has been considered antiferromagnetic. The mutual influence of the magnetic and chemical ordering is evidenced and a good agreement with the phase diagram is obtained. Our numerical results show that the magnetic order is able to increase the Kurnakov temperature and, reciprocally, the chemical order is responsible for a rise in the Curie temperature. Also, the influence of the applied magnetic field on the chemical order is investigated and an increase of the Kurnakov temperature with the external field is observed.     

Magnetic properties of a quasi-one-dimensional organic ferromagnet

A quasi-one-dimensional alternating-spin Heisenberg model is used to describe the charge-transfer organic ferromagnet, which is studied by the Green's function method. The magnetic properties of the charge-transfer organic ferromagnet in different temperature regions are obtained. A formula for the critical temperature T_c is obtained and is found to be related to the spin of donors, to the intrachain exchange interaction, and to the spatial anisotropy parameter. This conclusion can explain T_c of the organic ferromagnet. The spatial anisotropy parameter of the organic ferromagnet [FeCp₂¹][TCNE] we obtained is consistent with the estimated value of Narayan et al. The Curie-Weiss temperature Θ for the organic ferromagnet [CrCp₂¹][TCNE] we obtained is Θ = 15.6 K which is near the experimental result of θ = 22±1 K.     

Structure of polymer solutions at interfaces: a Monte Carlo simulation study

The canonical ensemble Monte Carlo method is applied to study the structure of polymer solutions confined between surfaces. The polymer molecules are modeled as fused-sphere freely rotating chains with fixed bond length and bond angles and the solvent as hard spheres. The simulation results for the configurational and conformational properties of the chains are presented with varying interfacial distances, chain concentrations, and chain lengths. The chains are depleted at the wall at lower density, which, however, becomes less at higher density. With an increase in the interfacial distance, the enhancement/depletion of the chains at the wall becomes more marked. At all interfacial distances and chain lengths, increasing the concentration of the solvent makes the oscillation in the density profile of the chains more pronounced. Conformational properties provide important indications regarding the behaviour of chains as they approach surfaces.     

Exact and Monte Carlo computations on a lattice model for change of conformation of a polymer

Conformational changes of linear polymers are studied by means of dynamic lattice models. The relaxation rates for the following four parameters describing the conformation of the polymer are studied for various polymer lengths: the square of the end-to-end distance, the square of the radius of gyration, thex component of the end-to-end vector, and the number of windings.In the most realistic models the relaxation rates for the first three of the above-mentioned properties decrease approximately proportional to the square of the number of monomers in agreement with the well-known Rouse model, while the relaxation of the winding number appears to be independent of the polymer length. The long-range interactions due to excluded volume restrictions are found to be of only minor importance compared to the rules presented for the local movements of the polymer segments.The results are obtained by diagonalizing the Markov matrix forn = 3, 4, 5, and 6 and by Monte Carlo simulation forn = 8, 16, 32, 64, and 128, wheren is the number of monomers.     

A green function approach to the paramagnetic phase of a Heisenberg ferromagnet

A higher-order decoupling similar to the first-order Bogolyubov-Tyablikov decoupling is used to find various correlation functions in the paramagnetic region for a Heisenberg ferromagnet. Expressions are given for the susceptibility, the nearest-neighbor correlation, and autocorrelation at the critical point as well as at high temperatures.This paper is based on the first author's Oxford University D. Phil, thesis. A preliminary account has been published elsewhere. (¹)     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

The magnetic properties of the two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field

The two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field is studied by means of the double-time Green's function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed.     

求解中子动力学方程的加权蒙特卡罗方法

为了实现基于蒙特卡罗方法的中子动力学计算,在传统的直接蒙特卡罗动力学方法的基础上,提出了一种加权蒙特卡罗动力学方法。该方法通过引入粒子权重的概念,隐式考虑中子俘获反应和裂变反应过程中中子数目的变化,避免了模拟粒子的数目随时间的变化,降低了统计偏差,消除了程序计算过程中粒子的存库操作,提高了计算精度。基于单能点堆模型,开发了中子动力学计算程序NECP-Dandi,进行了大量数值验证与分析,包括无缓发中子、单组缓发中子、六组缓发中子、正阶跃反应性引入、负阶跃反应性引入、正脉冲反应性、负脉冲反应性和正线性反应性引入等情况。数值结果表明,相比于直接蒙特卡罗动力学方法,加权蒙特卡罗动力学方法在计算结果的精度和计算效率上有较为明显的改进,程序结构更为简洁。     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.