The large N limit of the O(N) Heisenberg spin system in two dimensions

The large N limit of the O(N) Heisenberg spin system in two dimensions (a lattice version of the non-linear σ-model) is analysed by the collective field technique. A compact expression for the mass gap and the β-function is obtained for arbitrary but fixed gN. The strong and weak coupling limits of this expression correctly reproduce the known results.     

Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description

The problem of consistent Hamiltonian structure for O(N) nonlinear sigma model in the presence of five different types of boundary conditions is considered in detail. For the case of Neumann, Dirichlet and the mixture of these two types of boundaries, the consistent Poisson brackets are constructed explicitly, which may be used, e.g., for the construction of current algebras in the presence of boundary. While for the mixed boundary conditions and the mixture of mixed and Dirichlet boundary conditions, we prove that there is no consistent Poisson brackets, showing that the mixed boundary conditions are incompatible with all nontrivial subgroups of O(N).     

Steady-state scaling function of the (1 + 1)-dimensional single-step model

The steady-state height-height correlation function for the (1 + 1)-dimensional single-step model is calculated in a large-scale Monte Carlo simulation. Analysis of the data yields a universal ratio of scaling amplitudes which differs from the value obtained recently from a mode-coupling calculation. An empirical form for a universal scaling function is also presented.     

Perturbation theory predictions and Monte Carlo simulations for the 2D O(n) non-linear σ-models

By using the results of a high-statistics ( 10⁷) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear σ-model in 2 dimensions. We study the O(3) and O(8) models on large enough lattices to have a good control on finite-size effects. The magnetic susceptibility and three different definitions of the correlation length are measured. We check our results with large-n expansions as well as with standard formulae for asymptotic freedom up to 4 loops in the standard and effective schemes. For this purpose the weak coupling expansions of the energy up to 4 loops for the standard action and up to 3 loops for the Symanzik action are calculated. For the O(3) model we have used two different effective schemes and checked that they lead to compatible results. A great improvement in the results is obtained by using the effective scheme based on the energy at 3 and 4 loops. We find that the O(8) model follows very nicely (within few per mille) the perturbative predictions. For the O(3) model an acceptable agreement (within few per cent) is found.     

On the CP topological sigma model and the Toda lattice hierarchy

We propose, in bihamiltonian formalism, a version of the Toda lattice hierarchy that is satisfied by the two point correlation functions of the CP¹ topological sigma model at genus one approximation, and we also show that this bihamiltonian hierarchy is compatible with the Virasoro constraints of Eguchi–Hori–Xiong up to genus two approximation.     

The double Lagrangian its applications with U（1, J） symmetry and to the cosmology

By introducing the double complex scalar field, this paper constructs the double Lagrangian with the potential V（Ф（J）,Ф（J）） = V（│Ф（J）│）, which not only can describe the evolution of quintom Universe, but also can naturally give the spintessence and hessence Universe. Furthermore, the U（1, J） symmetry of the double complex Lagrangian is verified, and the total conserved charge within the physical volume is derived by means of the Norther theorem. Moreover, it can point out that the ＇imaginary motion＇ of the angular parameter in Ref.[14], in fact, is only a real phase displacement in our model.     

The structure and the potential energy function of AlSO(C_S,X~2A″)

By using the B3P86/aug-cc-pvtz method,the accurate equilibrium geometry of the AlSO(CS,X2A″) molecule has been calculated and compared with available theoretical values.The obtained results show that the AlSO molecule has a most stable structure with bond lengths of R OAl = 0.1864 nm,R OS = 0.1623 nm,R AlS = 0.2450 nm,together with a dissociation energy of 13.88 eV.The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics.The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time,which show the internal information of the AlSO molecule,including the equilibrium structure and stable point.The analysis demonstrates that the obtained potential energy function of AlSO is reasonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.     

Molecular multipoles and (hyper) polarizabilities from the Buckingham expansion:revisited

The Buckingham expansion is important for understanding molecular multipoles and (hyper) polarizabilities. In this study, we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series. Based on the derivation results, a general Buckingham expansion in the traced form is proposed, from which highly accurate numerical calculations using the finite field method can be achieved. The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient. The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.     

Four-dimensional N = 2 superstring constructions and their (non-) perturbative duality connections

We investigate the connections between four-dimensional, N = 2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector multiplets and hypermultiplets, with a gauge group of the maximal rank allowed in a perturbative heterotic string construction. We find evidence for duality between two type I compactifications recently proposed and a new heterotic construction that we present here. This duality allows us to gain insight into the non-perturbative properties of these models. In particular we consider gravitational corrections to the effective action.     

Structural, magnetic and transport properties of double perovskite compounds (Sr2−3xLa2xBax)FeMoO6

The crystal structure and magnetic properties of a series of ordered double perovskite oxides (Sr_2−3xLa_2xBa_x)FeMoO₆ (0x0.3) have been investigated. X-ray powder diffraction reveals that the crystal structure of the compounds changes from a tetragonal I4/m lattice to a cubic lattice around x=0.2. Though the nominal average size of the A site cation of (Sr_2−3xLa_2xBa_x)FeMoO₆ is designed to be almost independent of x, the refinements of the crystal structure show that the lattice constants increase with x in both the tetragonal and the cubic phase regions due to electron doping. As the x increases, the degree of cationic ordering on the B site is decreased pronouncedly, while the Curie temperature of the compounds is nearly unchanged. The saturation magnetization of the compounds decreases with x and shows a linear dependence on the degree of cation ordering. The resistivity of the parent compound shows a semiconducting behavior below room temperature, but those of the doped samples exhibit a metal–semiconductor transition. A correlation between the resistivity and metal-semiconducting transition temperature (T_M−S) is observed. The resistivity and T_M−S of the compounds decrease with x for x0.2 and increase for x0.2. Magnetoresistance of the compounds is reduced by the La/Ba doping. All these observations can be understood based on the interplay of the electron doping, change in bandwidth and the anti-site defect concentration.     

Energy crisis or a new soliton in the noncommutative CP(1) model?

The non-commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one [Phys. Lett. B 498 (2001) 277, hep-th/0203125, hep-th/0303090].

Due to the U(1) gauge invariance, the Seiberg–Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) θ-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are identical, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the “energy crisis”.

A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small.     

Structure,bonding and stability of semi-carbides M2C and sub-carbides M4C (M=V,Cr, Nb,Mo, Ta,W): A first principles investigation

Density functional theory within the generalized gradient approximation (GGA) is used to investigate the electronic structure and formation energies of semi-carbides M₂C and sub-carbides M₄C (where M=V, Cr, Nb, Mo, Ta and W). Our results show that M₂C carbides are more stable than M₄C. Total and partial densities of states were obtained and analyzed systematically for these phases. Moreover, the bonding nature of M₂C polymorphs is studied from the point of view of the Quantum Theory of Atoms in Molecules (QTAIM). It is found that inter-atomic interactions in these carbides are of mixed type including ionic, covalent and metallic components.     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

The relationship between crystal structure and electrical conductivity in the LaY1−xInxO3 (x=0.0–0.7) system

The electrical conductivity of the LaY_1−xIn_xO₃ (x=0.0–0.7) system has been studied from the viewpoint of crystal chemistry. The high temperature form of LaYO₃ (x=0.0) was ascertained to be the Sm₂O₃-type (B-type rare earth) structure, not perovskite-type one. The X-ray diffraction (XRD) experiments revealed that the samples with x=0.05 and 0.10 were the mixed phase of Sm₂O₃-type and perovskite-type structure, and changed to perovskite phase in the range of x0.20. From oxygen partial pressure dependence of the electrical conductivity, it was found that both the Sm₂O₃-type and the perovskite-type single phases showed hole conduction, but the mixed phase did oxide-ion one. The electrical conductivity of the LaY_1−xIn_xO₃ (x=0.0–0.7) system increased with increasing x, and showed the maximum value in the range of x=0.05–0.10, and then decreased with increasing x. The occurrence of oxide-ion conduction was discussed from the viewpoint of lattice distortion in the mixed phase.     

The structural,electronic, and magnetic properties of SrFeOn（n=2 and 2.5）： a GGA＋U study

Using density-functional calculations within the generalized gradient approximation (GGA)+U framework,we investigate the structural,electronic,and magnetic properties of the ground states of SrFeOn (n = 2 and 2.5).The magnetism calculations show that the ground states of both SrFeO2 and SrFeO2.5 have G type antiferromagnetic ordering,with indirect band gaps of 0.89 and 0.79 eV,respectively.The electronic structure calculations demonstrate that Fe cations are in the high-spin state of (dz2 )2(dxz,dyz)2(dxy)1(dx2 y2 )1(S = 2),unlike the previous prediction of (dxz,dyz)3(dxy)1(dz2 )1(dx2 y2 )1(S = 2) for SrFeO2,and in the high-spin state of (dxy,dxz,dyz,dx2 y2 ,dz2 )5(S = 5/2) for SrFeO2.5.     

Exact form factors in integrable quantum field theories: the sine-Gordon model (II)

A general model independent approach using the ‘off-shell Bethe Ansatz’ is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive Thirring model. Exact expressions of all matrix elements are obtained for several local operators. In particular soliton form factors of charge-less operators as for example all higher currents are investigated. It turns out that the various local operators correspond to specific scalar functions called p-functions. The identification of the local operators is performed. In particular the exact results are checked with Feynman graph expansion and full agreement is found. Furthermore all eigenvalues of the infinitely many conserved charges are calculated and the results agree with what is expected from the classical case. Within the frame work of integrable quantum field theories a general model independent ‘crossing’ formula is derived. Furthermore the ‘bound state intertwiners’ are introduced and the bound state form factors are investigated. The general results are again applied to the sine-Gordon model. The integrations are performed and in particular for the lowest breathers a simple formula for generalized form factors is obtained.     

Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory (ITP) of the dynamical mean field theory (DMFT) and coherent-potential approximation (CPA) is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix $t_{ij}^{mn} (m \ne n)$ are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.     

Electronic structure and charge distribution in : The ab initio approach

The full-potential linearized augmented plane wave (FP-LAPW) method was used for spin-polarized electronic structure calculations of stoichiometric superconductor. The generalized gradient approximation plus Hubbard correction (GGA + U) was employed for electrons. The reference calculations of were carried out in the spin-polarized mode to enable direct comparison. The determined total and atomic-projected densities of states (DOS), as well as charge distribution and on-site magnetic moments were analyzed and compared in detail. It was shown that in Dy123 system DOS in the close vicinity of the Fermi level is higher than in Y123. Also more efficient transfer of charge from CuO₂ planes was noticed in Dy123. The strongly localized magnetic spin moment of Dy is responsible for relatively weak magnetic interactions in the system, mostly in the CuO₂ planes. The obtained computational results are in agreement with the reported good superconducting properties of DyBa₂Cu₃O₇ compound.     

The thermodynamic Bethe ansatz and the 1/N correction to the density phase transition in the Gross-Neveu model

We compute the 1/N correction to the location of the previously found first-order phase transition in the Gross-Neveu model at a chemical potential where m is the fermion mass. We employ an expression for the free energy f(μ) given by the thermodynamic Bethe ansatz under the approximation that the fundamental fermions dominate the ground state, and combine it with the effective potential evaluated at zero chemical potential.

Our result is .     

U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.