Variational Cumulant Expansion Study of Z(N) Lattice Gauge Theory with Symanzik's Improved Action

With the variational cumulant expansion (VCE) method, the internal energy and the specific heat of the Z(N) lattice gauge theory with Symanzik's improved action are calculated up to the third order. The variational parameter is determined by the main valued method and the result is compared with the VCE result for standard Wilson action. Furthermore, the changes are compared with those of the SU(2) case.     

多层伊辛膜的磁学性质

用变分累积展开(VCE)方法的一阶近似计算了包括最近邻和次近邻作用的多层伊辛膜的磁学 性质,导出了自发磁化强度、矫顽力、居里点、奈尔点、顺磁磁化率及分子场系数与层数的关系表达式,并做了数值计算和讨论. 关键词： 多层膜 伊辛模型 磁化     

Analysis and Discussion About How to Determine the Variatiotnal Parameters in the Variational-Cumulant Expansion

Four methods of determining the variational parameter in the varia tional-cumulant expansion (VCE) are studied on the 2-dimensional Ising model. A comparison with the exact result shows that the main-variation method is the best one at low temperature, the completevariational method is better than others at high temperature, the accumulation-point method is the best one to approximate the intermediate coupling region, and each of the methods is analyzed from the original formulas or conjectures. Some suggestions are given in order to get optimal results. The VCE is also analyzed Gom a point of view of symmetry breaking for the first time.     

Variat ional-Cumulant Expansion on the Five-State Clock Model

The phase transition of the 5-state dock model has been studied by standard variationalcumulant expansion (VCE) method. We calculated the fiee energy (F) and the internal energy (E) to the fourth order approximation and the specific heat (C) to the third order approximation with the trial action of one variational parameter. The position of the phase transition point given above is in agreement with the results of the Monte Carlo (MC). We also calculated the model to the third order approximation with the trial action of two variational parameters. The comparison of the results for one variational parameter with that for two is given. From this, we can see how the choice of the trial action affects the result and the trial action must be equivalent to the action of the system. All above has shown that the VCE is convergent in the calculation of the 5-state clock model.     

Analytical study of Lattice U(1) and U(1)-Higgs Models at Finite Temperature With Symanzik Action

The lattice U(1) and U(1) -Higgs models with Symanzik action are analytically studied at finite temperature using variational cumulant expansion (VCE). The Polyakov lines and the critical index β are calculated. The results show that VCE of system with Symanzik action converges more rapidly than that of Wilson action.     

Analytical Characters of 2-Dimensional Ising Model with Variat ional-Cumulant Expansion to the Seventh order

In order to investigate the variational-cumulant expansion (VCE) method, the 2-dimensional Ising model is expanded to the seventh order by adopting the method of enumerating connected diagrams, in whose process, how to determine the variational parameter is analyzed. The internal energy (U), specific heat (C) and spontaneous magnetization (M) are calculated from the first order to the seventh order. The results show that the thermodynamic and magnetic quantities converge to the exact values very quickly and the critical point approaches the exact one order by order. The curve-pairing phenomenon is watched between neighboring order curves at high teinperature region.     

Analytical Study of the Antiferromagnetic Heisenberg Films

With the variational cumulant expansion (VCE) method, the thermodynamic behaviors of S = 1/2 antiferromagnetic Heisenberg films in simple cubic lattices are studied analytically. From the analytic properties of the free energy, in principle we are able to calculate analytically the critical temperatures T_c(L) and the thermodynamic functions, to any order cumulant as the functions of the number of L (the hyperlayers in the hyperfilm). Explicit expressions for T_c(L) up to the fourth order are given. A comparison with the existing results for 3-dimensional system is given. The effective range of the interactiori is obtained from numerical results.     

Magnetic Properties of Heisenberg Thin Films in an External Field

The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.     

A New Approach about Determining the Phase Transition Point in Variational-Cumulant Expansion

Based on Variational-cumulant expansion (VCE), through calculating Polyakov line in the SU(2) gauge model at finite temperature and considering the similarity of finite size interaction in VCE method with the finite volume effect in Monte Carlo (MC) simulation, a new approach is adopted to determine the critical couplings for the deconfinement phase transition. New results of VCE which are close to MC data manifest that new approach is much more effective than the traditional one and show that VCE analysis is consistent with MC simulation.     

变分累积展开方法中确定相变点的新方法

在计算有限温度SU(2)格点规范模型Polyakov线的过程中,考虑到变分累积展开法中有限距离相互作用效应与Monte Carlo中的有限体积效应的相似性,采用了新的方法来确定相变点.与已有的方法以及Monte Carlo模拟给出的结果比较,新方法给出的结果更接近Monte Carlo结果.     

Magnetic Properties of Heisenberg Thin Films in an External Field

The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.     

An Analytical Study of the d-Dimensional q-State Potts Models on Lattice

We investigate the phase structure of the d-dimensional q-state Potts models on lattice by the variational cumulant expansion (VCE) approach, we calculate the internal energy and specific heat for this model. Specially, we give the results for 2-dimensional q = 4,5,6 states Potts models. A comparison with Monte Carlo (MC) data is also presented. Our formalism can give the results for Potts models in any dimensionality d and any states q straightforwardly.     

一个用于变分累积展开计算的MATHEMATICA软件包(VCE1.0)

利用MATHEM ATICA软件包的符号运算功能,发展了一个在计算机上实现对含近邻相互作用的格点模型进行变分累积展开研究的程序包(VCE1.0)。高阶连接图的计数及自由能等的解析表达式都可用这个程序包直接得到。该程序包可用于一大类格点规范理论与统计物理模型的相结构的研究。     

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T _KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T _KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T _KT as a function of the easy-plane anisotropies and exchange interactions. Received 3 April 2001 and Received in final form 20 September 2001     

Phase Structures of U(l) and SU(2) Lattice Gauge Models at Finite Temperature

With the variational-cumulant expansion (VCE) method, the phase structures of the U(1) and SU(2) lattice gauge models at finite temperature are studied. The order parameter Polyakov line with N_T = 2 is calculated to the fourth order. For the U(1) and SU(2) lattice gauge models in D = 3 + 1 and D = 2 + 1 at finite temperature, the results show the existence of the second order phase transition.     

Kosterlitz-Thouless phase transition in microcavity polariton system

The Kosterlitz-Thouless phase transition in a system of exciton-polaritons in a microcavity is studied. The transition temperature to superfluid state was found as a function of exciton-photon detuning. A nonquadratic dispersion law was taken into account in the framework of the self-consistent harmonic approximation (SCHA). The text was submitted by the authors in English.     

The Critical Temperature of Quantum Spin Model Determined with Variational-Cumulant Expansion

The variational-cumulant expansion (VCE)methodis used to calculate the quantum XY model, for which the trial action S₀ does not commute with the action S, with arbitrary magnitude of spin on various one-, twe and three-dimensional lattices. The free energy of the model is expanded to the third order and the analytical formulae of critical temperature T_c are given for each order. To testify this method in a wider range, the Heisenberg model on different lattices is also calculated, which has more comparable results. Weighted fitting method of statistical mathematics is adopted to predict T_c of infinite order.     

Variational analysis of the disc-loaded waveguide slow-wave structures

The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calculated by the variational method. Then the dispersion characteristics of slow-wave structures are obtained using lossless microwave quadrupole theory. Good agreement was observed between results of the variational method and those of field matching method and high frequency structure simulator. In the case of broad band, results of the variational method are better than those of field matching method.     

A comparison of approximate methods for solving non-conservative problems of elastic stability

The methods of Ritz, Galerkin, and complementary energy are applied to a nonconservative problem in the theory of elastic stability. The numerical calculations are based upon (i) a variational expression, for which no functional can be determined, and (ii) an adjoint variational principle, for which a functional is established in terms of the variables of the original non-self-adjoint eigenvalue problem and the adjoint problem. The adjoint variational principle yields somewhat more accurate values for the critical load parameter than does the variational expression. In addition, the results obtained by means of the complementary energy method are more precise than the corresponding results obtained from the Ritz and Galerkin methods.     

Variational-Cumulant Expansion up to the Sixth Order Approximation on 2-Dimensional Ising Model

To study the variational-cumulant expansion (VCE) method, the 2-dimensional Ising model has been selected. The model is evaluated to the sixth order approximation with a scheme for the enumeration of connected diagrams. The internal energy (U), specific.heat (C) and spontaneous magnetization (M) have been calculated. A comparison with the exact results shows that thermodynamic and magnetic quantities converge to the exact values rather quickly and the position of phase transition point approaches to the exact pointstand order by order.