Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation S ₀ S _r decreases asymptotically asr ^–1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this superfrustration on the free energy and on the ground state properties is also discussed.     

Comments on the presence of a peak in the static structure factor of an electron liquid

Emphasis is laid on the fact that the peak in the static structure factor S(k) observed in a recent experiment at k≈2k_F for conduction electrons in beryllium agrees well with the one predicted by us theoretically some time back. The error in the calculation of the pair correlation function g(r) using the experimental data on S(k) is pointed out. The position of the peak obtained in our g(r) clearly indicates that the effect of electron correlation is to condense into a Wigner lattice at a distance equal to the average interparticle separation rather than making a Mott type transition to an atomic-like state.     

Electron paramagnetic resonance linewidth in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons

Electron magnetic relaxation was studied in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons. The electron paramagnetic resonance (EPR) linewidth (Г_⊥) was calculated at temperatures T≤J (J is the nearest-neighbor interaction constant). The magnitude of Г_⊥ caused by the Dzyaloshinskii-Moriya interaction is shown to grow as r ₀/a with decreasing temperature, whereas the anisotropic symmetric interaction leads to the (r ₀/a)³ dependence, where r ₀ is the average size of a skyrmeon and a is the lattice parameter. The results obtained agree qualitatively with calculations performed on the basis of a renormalization-group (RG) analysis of the nonlinear σ model at .     

Structure of higher order corrections to the Lipatov asymptotic form

High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations, or instantons, of the corresponding functional integrals. For most field theories, the Lipatov asymptotic form has the functional form ca ^NΓ(N+b) (N is the order of perturbation theory) and the relative corrections to it are series in powers of 1/N. It is shown that this series diverges factorially and its high-order coefficients can be calculated using a procedure similar to the Lipatov one: the Kth expansion coefficient has the form const[ln(S ₁/S ₀)]^?K Γ(K+(r ₁? r ₀)/2), where S ₀ and S ₁ are the values of the action for the first and second instantons of this particular field theory, and r ₀ and r ₁ are the corresponding number of zeroth-order modes; the instantons satisfy the same equation as in the Lipatov method and are assumed to be renumbered in order of their increasing action. This result is universal and is valid in any field theory for which the Lipatov asymptotic form is as specified above.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K_c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although dimethylsulfoxide is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r) but the least-squares system of normal equations is better conditioned with representation I^r. These results are compared to those obtained for a few typical molecules.     

Understanding cooperative behavior in structurally disordered populations

The effects of an inhomogeneous competing environment on the extent of cooperation are studied within the context of a site-diluted evolutionary snowdrift game on a square lattice, with the occupied sites representing the players, both numerically and analytically. The frequency of cooperation ?_C generally shows a non-monotonic dependence on the fraction of occupied sites ρ, for different values of the payoff parameter r. Slightly diluting a lattice leads to a lower cooperation for small and high values of r. For a range of r, however, dilution leads to an enhanced cooperation. An analytic treatment is developed for?_C^I + ?_C^II, with?_C^I emphasizing the importance of the small clusters of players especially for?_C^II from the other players is shown to be inadequate. A local configuration approximation (LCA) that treats the local competing configurations as the variables and amounts to include spatial correlation up to the neighborhood of a player’s neighbors is developed. Results of ?_C (ρ) and the number of different local configurations from LCA are in good agreement with simulation results. A transparent physical picture of the dynamics stemming from LCA is also presented. The theoretical approach provides a framework that can be readily applied to competing agent-based models in structurally ordered and disordered populations.     

Reconditioning in Discrete Quantum Field Theory

We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x ₀,r) where x ₀ and r are positive integers representing time and maximal total energy, respectively. The operator S(x ₀,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x ₀,r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each (x ₀,r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.     

Particle mixing and charge asymmetric nuclear forces

The charge asymmetric effect of ?ω and πη electromagnetic mixing on the ¹S₀ NN potential is reviewed. It is found that the ?ω contribution dominates and leads to an n-n potential which is more attractive than the p-p potential. The shift in the scattering lengths is then calculated to be |a_nn|?|a_pp| ≈ 0.9 fm and the shift in effective ranges is r_nn?r_pp ≈ ?0.02 fm.     

Dynamical Arrest,Tracer Diffusion and Kinetically Constrained Lattice Gases

We analyze the tagged particle diffusion for kinetically constrained models for glassy systems. We present a method, focusing on the Kob–Andersen model as an example, which allows to prove lower and upper bounds for the self-diffusion coefficient D _S. This method leads to the exact density dependence of D _S, at high density, for models with finite defects and to prove diffusivity, D _S > 0, at any finite density for highly cooperative models. A more general outcome is that under very general assumptions one can exclude that a dynamical transition, like the one predicted by the Mode-Coupling-Theory of glasses, takes place at a finite temperature/chemical potential for systems of interacting particle on a lattice.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the ¹ S ₀ state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the ¹ S ₀ state, the following values were obtained for the neutron-neutron scattering length and effective range: a _nn = ?16.59(117) fm and r _nn = 2.83(11) fm. The calculated values agree well with present-day experimental results.     

Interatomic force constants studies of AMF3perovskite-type crystals (A = K,Rb; M = Mg,Ni, Co,Zn, Mn)

A simple model involving only three force constants allows us to evaluate the short range interactions in perovskite fluorides from the experimental values of the elastic constants and the lattice parameters of these compounds. The results indicate that the A-F bonds are quite central in character whereas the M-F bonds are axially symmetric; thus the short range A-F interactions are assumed to have the Born-Mayer form:ZZZZZBy studying the variations of the force constants with respect to the lattice parameter r, it is determined that ρ = 0·232 , λ = 2·8 × 10^?8 ergs for K⁺-F^?; ρ = 0·232 , λ = 4·1 × 10^?8 ergs for Rb⁺-F^?; λ₂, ρ₂ and ρ₂ are respectively 6·9 × 10^?10 ergs, 0·34 , 0·98for Co²⁺-F^? and 2·9 × 10^?10 ergs, 0·46 , 1·40for Mn²⁺-F^?. Taking into account both the short range repulsive potential and the long range electrostatic potential we can study the variations of the lattice energy as a function of r near the equilibrium position and deduce a theoretical value of the lattice distance. In spite of the simplicity of the model, the discrepancy between the experimental and the theoretical values is less than 10 per cent for all the compounds.     

Correlation analysis of the shifts of the electronic spectra of anthracene, phenanthrene, and fluorene as functions of the temperature in the gas phase and of the refractive index in n-paraffin solvents

The temperature-induced shifts of the maxima of the longest-wavelength bands of the S ₁ ← S ₀ and S ₂ ← S ₀ transitions in phenanthrene and the S ₁ ← S ₀ transition in fluorene in the gas phase are measured. A correlation analysis of these data and similar data on the S ₁ ← S ₀ and S ₁ → S ₀ transitions in anthracene is fulfilled. The positions of the maxima of analogous bands of the S ₁ ← S ₀ transition in anthracene, S ₁ ← S ₀ and S ₂ ← S ₀ transitions in phenanthrene, and S ₁ ←S ₀ transition in fluorene dissolved in liquid n-paraffins are also measured and analyzed as functions of (n ² ? 1)/(n ² + 2), where n is the refractive index of the solvent. The results confirm the conclusion of the Mirumyantz-Demchuk theory about the linear temperature dependence of the wave number of a band maximum but contradict the prediction that, upon extrapolation to T = 0 K, the positions of the maxima correspond to the electronic transitions in the molecule unperturbed by out-of-plane vibrations of the aromatic core.     

ΛN and ΣN Interactions from Lattice QCD

We present our recent study on ΛN and ΣN (isospin I = 3/2) interactions by measuring Nambu–Bethe–Salpeter wave functions on the Lattice QCD. The lattice QCD calculation is performed by using the N _f  = 2 + 1 gauge configurations generated by PACS-CS collaboration together with employing an improved method to obtain potentials in lattice QCD simulations. For the ¹ S ₀ channel, the central ΣN (I = 3/2) potential and the central ΛN (¹ S ₀) potential are found to be very similar. For the spin triplet (³ S ₁?³ D ₁) channels, the central ΛN(³ S ₁?³ D ₁) potential is attractive while the central ΣN(I = 3/2, ³ S ₁?³ D ₁) potentials is repulsive. Tensor potentials, on the other hand, are rather weak in both ΛN and ΣN(I = 3/2) systems.     

光子晶体波导中的孤子传输及其延迟特性研究

研究了正方晶格和三角晶格空气背景硅介质柱光子晶体线缺陷波导导模左带隙边缘处的亮孤子脉冲传播特性及其慢光延迟特性. 采用平面波展开法仿真分析了波导相邻两行介质柱大小r₁和r₂以及波导宽度D对孤子脉冲传输所需峰值功率P₀和延迟时间T_s的影响,总结了其变化规律. 通过调整波导结构得到了正方晶格和三角晶格优化波导结构,优化后,正方晶格结构波导P₀减小了81.17%,T_s增加了66.32%;三角晶格结构波导P₀减小了73.7%,T_s增加了67.63%,实现了孤子传输性能的大幅度优化. 关键词： 光子晶体波导 光孤子 峰值功率 延迟时间     

Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.