THE MC CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

By combining Monte Carlo method and variational method,we calculate the mass gap of SU(2) lattice gauge theory in 18*18 lattice of 2+1 dimensions by means of the icosaheral subgroup (Y120) using a hamiltonian of which the ground state is exactly known.In the range 0<1/g²,we obtain the results which are in good agreement with analytical calculation of SU(2) group.The scaling behaviour of mass gap am=2.3g² is confirmed.     

MONTE CARLO RENORMALIZATION GROUP STUDY OF φ4 MODEL

The Monte Carlo renormalization group method proposed by Callaway is applied to φ⁴ model on two dimensional triangle lattice.The flow diagram,fixed point and critical exponent are determined,There is no fixed point in the range of 0.1<λ<10⁹.The large λ limit,as expected,is consistent with the Ising model.     

Structural and magnetic properties of Cr1+x(Se1−yTey)2 compounds

The structural and magnetic properties of Cr_1+x(Se_1−yTe_y)₂ having a NiAs structure has been studied for (1+x)=1.27, 1.32 and 1.36 and y=0.75 by means of the Korringa-Kohn-Rostoker (KKR) band structure method. The sub-stoichiometry and the disorder on the chalcogenide sub-lattice has been treated by means of the coherent potential approximation (CPA) alloy theory. From total energy calculations a preferential site occupation on the Cr sub-lattice was found together with an antiparallel alignment of the magnetic moments on the two inequivalent Cr layers. The magnetic properties at finite temperature has been studied by means of Monte Carlo simulations on the basis of a classical Heisenberg Hamiltonian and the exchange coupling parameters calculated from first principles. This approach allowed to determine the critical temperature in good agreement with experiment.     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL U(1) LGT

We present a variational calculation of 0^+－ and 0⁺⁺ glueball masses in 2+1 dimensional U(1) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct classical continuum limit.In deep weak coupling region,we obtain that am(0^+－) decreases with 1/g² exponentially and am(0⁺⁺)=2.78g².     

THE MASS GAP IN 2+1 DIMENSIONAL SU(3) LATTICE CAUGE THEORY

We present a variational calculation of C=+1 and C=－1 glueball masses in 2+1 dimensional SU(3) lattice gauge theory using a Hamiltonian in which the ground state is exactly known.In the range 0<1/g²≤6,we obtain good scaling behaviour am₊=36.1g² and am_－=5.98g².     

Monte Carlo study of the two-step spin transition in [FeXZn1∓X(2-pic)3]Cl2 · EtOH

The Monte Carlo method has been applied to reproduce the two-step spin transition in [Fe_xZn_1?x(2-pic)₃]Cl₂ · EtOH (2-pic = 2-picolylamine). The partition function of the Hamiltonian has been factorized in two parts describing the inner degrees of freedom of the spin transition molecules and the interaction between them. The factorization is equivalent to an effective Hamiltonian which can be mapped on an Ising system in an applied magnetic field. The interaction consists of an infinite range and a short range interaction part. Qualitatively the two-step transition under pressure and the Zn diluted system have been well reproduced with infinite range and the next nearest neighbour interaction of ferromagnetic type and the nearest neighbour interaction of antiferromagnetic type in a simple cubic lattice.     

THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian with the ground state being exactly known is made.In the range 0≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory.     

Statistical mechanics of cation ordering in PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

A model Hamiltonian for B cation ordering (Sc-Nb(Ta)) in PbSc_1/2Nb_1/2O₃ and PbSc_1/2Ta_1/2O₃ solid solutions is constructed. The parameters of the model Hamiltonian are determined from the ab initio calculation within the ionic crystal model with allowance made for the deformability and the dipole and quadrupole polarizabilities of the ions. The temperatures of the phase transition due to the ordering of the B cations are calculated by the Monte Carlo method in the mean-field and cluster approximations. The phase transition temperatures calculated by the Monte Carlo method (1920 K for PbSc_1/2Ta_1/2O₃ and 1810 K for PbSc_1/2Nb_1/2O₃) are consistent with the experimental data (1770 and 1450 K, respectively). The thermodynamic properties of the cation ordering are investigated using the Monte Carlo method.     

(3 1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1 1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3 1)-dimensional harmonic oscillator.``     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LGT

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct continuum limit is made.In the range 1.3≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory and the results obtained by another Hamiltonian which does not possess correct continuum limit.     

Glueball Masses of the 0++ and 0－－ in 3+1-D SU(3) LGT

We improve the coupled cluster method in lattice gauge theory based on the application of the random phase approximation. Using this method, we study the vacuum wavefunction and glueball mass of the 0^－－ and 0⁺⁺ in 3+1 D SU (3) lattice gauge theory by finding the solution of the Hamiltonian eigenvalue equation. The calculated results are satisfacting γ=m (0－－)/m(0++)=1.8578±0.0506.     

A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour

The quantum version of a non-linear oscillator, previously analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx²)⁻¹ and with a λ-dependent non-polynomial rational potential. This λ-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for λ → 0 all the characteristics of the linear oscillator are recovered. First, the λ-dependent Schrödinger equation is exactly solved as a Sturm-Liouville problem, and the λ-dependent eigenenergies and eigenfunctions are obtained for both λ > 0 and λ < 0. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as λ-deformations of the standard Hermite polynomials. In the second part, the λ-dependent Schrödinger equation is solved by using the Schrödinger factorization method, the theory of intertwined Hamiltonians, and the property of shape invariance as an approach. Finally, the new family of orthogonal polynomials is studied. We prove the existence of a λ-dependent Rodrigues formula, a generating function and λ-dependent recursion relations between polynomials of different orders.     

Experimental Sensitivities on Searching for Rare and Forbidden Decays of Charm Mesons at BES-III

We discuss the Monte Carlo studies of searching for the rare and forbidden pure-leptonic and semi-leptonic decays of D^+,0 and D⁺_s mesons, based on a full Monte Carlo simulation for the BES-III detector, with the BES-III Offline Software System. The experimental sensitivities of searching for 36 rare and forbidden charm meson decays are estimated.     

A statistical approach to quantum mechanics

A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x_i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, |ψ₀(x)|², the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.     

Study of ferroelectric phase transitions in disordered PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

Ferroelectric phase transitions and thermodynamic properties of disordered PbSc_1/2Ta_1/2O₃ and PbSc_1/2Nb_1/2O₃ solid solutions have been investigated by the Monte Carlo method. The parameters of the effective Hamiltonian were calculated within the generalized Gordon-Kim model. The obtained values of the phase-transition temperatures and spontaneous polarization are in satisfactory agreement with the experimental data.     

Thermal conductivity of La0.67(CaxSr1−x)0.33MnO3 (x=0, 0.5, 1) and La0.6Y0.07Ca0.33MnO3 pellets between 10 and 300 K

Thermal conductivity (λ) of nanocrystalline La_0.67(Ca_xSr_1−x)_0.33MnO₃ (x=0, 0.5, 1) and La_0.6Y_0.07Ca_0.33MnO₃ pellets prepared by a novel ‘pyrophoric’ method have been studied between the temperature range 10 and 300 K. Our data show that the magnitude of thermal conductivity is strongly influenced by the ion substitutions at La-site. The analysis of the thermal conductivity data indicates that the thermal transport is governed largely by phonons scattering in these systems and the electronic contribution is as small as 0.2-1% of total thermal conductivity (λ_total). At low temperatures (<90 K) 2D like lattice defects contribute to the phonon scattering dominantly and its strength increases with increasing Sr content and also with partial substitution of La by Y. Depending upon the composition of the samples, the magnon thermal conductivity contributes 2-15% of λ_total close to T_C. In the paramagnetic regime the unusual increase in λ_total keeps signature of large dynamic lattice distortion.     

Magnetostriction, Curie temperature and microstructure of Tb0.29(Dy1−xPrx)0.71Fe1.97 oriented alloys

The Tb_0.29(Dy_1−xPr_x)_0.71Fe_1.97 (x=0, 0.1, 0.2 and 0.3) alloys were prepared by directional solidification method. The orientation, magnetostriction λ, Curie temperature T_c and microstructure of alloys were characterized by XRD, standard resistant strain gauge technique, VSM and SEM-EDS. The results reveal that the alloys have a preferred orientation of 〈1 1 0〉 and 〈1 1 3〉 direction when x>0. With the increase in Pr content, the T_c of alloys decreases gradually and the non-cubic phase appears, resulting in the decline of λ dramatically, from 1935.2×10⁻⁶ for x=0 to 695.9×10⁻⁶ for x=0.3 at a compressive stress of 6 MPa and a magnetic field of H=240 kA m⁻¹.     

Statistical mechanics of cation ordering and lattice dynamics of PbZr<Subscript>x</Subscript>Ti<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> solid solutions

An effective Hamiltonian for Zr-Ti cation ordering in PbZr_xTi_1?xO₃ solid solutions is written out. To determine the parameters of the effective Hamiltonian, a nonempirical calculation is performed within an ionic-crystal model taking into account the deformation and dipole and quadrupole polarizabilities of ions. The thermodynamic properties of cation ordering are studied using the Monte Carlo method. The calculated phase transition temperatures (180 and 250 K for the concentrations x=1/3 and 1/2, respectively) are much lower than the melting temperature of the compound under study. At such temperatures, the ordering kinetics is frozen and, in reality, the phase transition to the ordered phase does not occur, in agreement with experimental observations. Within the same ionic-crystal model, we calculated the high-frequency permittivity, Born dynamic charges, and the lattice vibration spectrum for a completely disordered phase and certain ordered phases. It is shown that soft vibration modes, including ferroelectric ones, exist in the lattice vibration spectrum of both the completely disordered and the ordered phases.     

Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.