Monte Carlo simulation of a lattice gas model of multilayer adsorption

A lattice gas model of physical adsorption of atoms on a periodic substrate has been studied using Monte Carlo simulations. Adsorption isotherms and layer coverage isotherms are determined and from these we find distinct phase boundaries for transitions on successive layers. In contrast to mean field results our data suggests that the critical temperature increases only slowly with increasing layer number, and appears to approach the roughening temperature for infinite layer number.     

Ground state of a spin system with two- and four-spin exchange interactions on the triangular lattice

We study a spin system with both two- and four-spin exchange interactions on the triangular lattice as a possible model for the nuclear magnetism of solid ³He layers adsorbed on grafoil. The ground state is analyzed by the use of the mean-field approximation. It is shown that the four-sublattice state is favored by introduction of the fourspin exchange interaction. A possible phase transition at a finite temperature into a phase with the scalar chirality is predicted. Application of a magnetic field is shown to cause a variety of phase transitions.     

Dynamical generation of a Coulomb phase in the mean-field approach to Z(N) lattice gauge theories

The phase diagram of Z(N) lattice gauge theories is examined in the mean-field approach. It is shown how large non-perturbative fluctuations around the mean-field may naturally occur in these theories. When this happens, a massless phase which is absent in the mean-field approximation is dynamically generated. An order parameter which characterizes the Coulomb to Higgs phase transition is introduced. The predictions for the values of the critical coupling for this transition are in excellent agreement with the Monte Carlo data in four dimensions.     

First-order phase transition and phase coexistence in a spin-glass model

We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with random magnetic interaction. The thermodynamics is worked out in the full replica symmetry breaking scheme. The model exhibits a high temperature/low density paramagnetic phase. As temperature decreases or density increases, a phase transition to a full replica symmetry breaking spin-glass phase occurs. The nature of the transition can be either of the second order or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter, a latent heat, and coexistence of phases.     

Concentration fluctuations in adsorbed layers

The temperature and coverage dependence of the mean square concentration fluctuations in a small open domain of an adsorbed layer is discussed for various situations. It is shown that fluctuations decrease with increasing temperature and reach a limiting value when attractive interactions predominate, but increase and reach a limiting value when repulsive interactions predominate, if a single non-ideal two -dimensional phase exists. Deviations from ideal gas behavior are strongest at half coverage. At very low coverage (low particle concentration) and very high coverage (low hole concentration) ideal behavior is approached. If the layer consists of a two phase system, for instance a two-dimensional liquid or solid in equilibrium with a two-dimensional gas, fluctuations far below the critical temperature are dominated by fluctuations in the partition between phases. As the critical temperature is approached fluctuations first decrease because the mean concentrations in the two phases approach each other, and then increase very sharply near T_c. Detailed calculations for the single phase situation are given for several approximations: a dilute gas; a mean field approximation; a lattice gas in both the Bragg-Williams and the BethePeierls-Weiss approximations. The latter which takes some account of correlations between adsorbate particle positions seems to explain reasonably the presently available experimental observations on chemisorbed layers.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.     

On the competition between magnetic order and local Kondo effect in Kondo lattice

We investigate the competition between magnetic order and local Kondo effect in a Kondo lattice model (i.e. the Coqblin-Schrieffer Hamiltonian extended to a lattice) in a mean-field approximation, taking account of the spin-orbit degeneracy of each localized f level. This leads to the definition of a dependent Kondo temperature. We study the Kondo phase and compare its energy with the energies of magnetic phases, when the number of the conduction band electron per site is near one. We present a phase diagram which shows the occurrence of three phases: Kondo, antiferromagnetic and paramagnetic phases. Our model in the mean-field approximation also shows a somewhat flat Kondo temperature, for large values of , as a function of the exchange coupling J between conduction and localized f electrons. Finally we show some scaling effects between and J and we define a corresponding Kondo temperature. Received 21 September 1998 and Received in final form 8 February 1999     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

Scaling property of the critical hopping parameters for the Bose-Hubbard model

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d ≥ 2. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical parameters for d ≥ 2 and any g with high accuracy.     

FERRIMAGNETIC PHASES OF THE BLUME-EMERY-GRIFFITHS MODEL AND THE POTTS MODEL ON THE DIAMOND LATTICE

The phase transitions in the Blume-Emery-Griffiths (BEG) model and antiferromagnetic Potts model on the diamond lattice are investigated using the cluster-variation method in the pair approximation. The ferrimagnetic phases are found to be different from those on the simple-cubic lattice. The phase diagrams of the BEG model are also calculated. In the vicinity of the parameter line where the BEG model reduces to the three-state antiferromagnetic Potts model, new types of phase diagram are obtained. The results are different from those of the mean-field theory, which is a good approximation only for large coordination number of the lattice.     

参数修改对铁电薄膜相变性质的影响

在关联有效场理论的框架内, 利用微分算子技术, 详细地计算了基于横场伊辛模型描述的对称铁电薄膜系统的相变性质. 根据薄膜各层自旋平均值构成的一系列耦合方程, 推导出可以用来计算任意层的具有不同表面层的薄膜相图的解析通式方程, 讨论了参数修改对薄膜相互作用参数从FPD (铁电相占主导地位的相图)到PPD (顺电相占主导地位的相图)过渡值和参数空间中各相变区域的影响. 在与平均场近似进行比较的结果显示, 关联有效场理论所得到的铁电薄膜的铁电性在某种程度上比平均场近似下的结果减弱. 关键词： 铁电薄膜 横场伊辛模型 相图 居里温度     

Density fluctuations in the presence of spinodal instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.     

A simple approximation for Ising spin models

A simple method is introduced for Ising spin systems based on the correlated molecular-field theory. Here, we consider an interacting triple in the mean field of its surrounding lattice points taking into account the product of three spins in the cluster. The present results for Curie temperature are compared to the mean-field theory(MFT), Bethe–Peierls–Weiss(BPW) approach, and self-consistent correlated field(SCCF) approximation, respectively. A procedure of triangular clusters is investigated that yields very distinguishable improvement of the critical temperature, as well.     

Concentration profiles of binary multi-layer films in non-equilibrium state

The time evolution of the concentration profile in a binary multi-layer film is investigated by using the Cahn-Hilliard equation, which is obtained on a basis of the lattice gas model treated within the framework of the layered mean-field approximation. For binary alloys with some ordered structures in the bulk equilibrium phase diagram, it is found that the corresponding structures appear and/or disappear with time, and then the system attains the thermal equilibrium state after an infinite time. It is also found that the time evolution strongly depends on the initial state.     

The mean-field approximation in the SU(2) pure lattice gauge theory

The phase structure of the SU(2) pure lattice gauge theory with two coupling constants is derived in the mean-field approximation. The obtained phase diagram agrees with Monte Carlo results. The technique used here allows the computation of further corrections.     

Mean-field approximation for the potts model of a diluted magnet in the external field

The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998