On long-range order in low-dimensional lattice-gas models of nematic liquid crystals

The problem of the orientational ordering transition for lattice-gas models of liquid crystals is discussed in the low-dimensional case d = 1, 2. For isotropic short-range interactions, orientational long-range order at finite temperature is excluded for any packing of molecules on the lattice Z^d; on the other hand, for reflection-positive long-range isotropic interactions, we prove the existence of an orientational ordering transition for high packing (μ > μ₀) and low temperatures (β > β_c(μ)).     

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is non-negative and vanishes above a wave number K(0) are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three-dimensional example is an interaction of asymptotic form cosK(0)r/r(4). The result is obtained for densities rho > or = rho(d), where rho(1) = K(0)/2(pi), rho(2) = (sq.rt(3)/8)(K(0)/pi)(2), and rho(3) = (1/8sq.rt(2)) x (K(0)/pi)(3). At rho(d) there is a unique periodic GSC which is the uniform chain, the triangular lattice, and the bcc lattice for d = 1,2,3, respectively. For rho > rho(d), the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K(0), and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho > or = (1/6 sq.rt(3)) x (K(0)/pi)(3).     

A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models

We study families of dependent site percolation models on the triangular lattice and hexagonal lattice that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on .The work was conducted while this author was at Department of Physics, New York University, New York, NY 10003, USA. Research partially supported by the U.S. NSF under grants DMS-98-02310 and DMS-01-02587.Research partially supported by the U.S. NSF under grants DMS-98-03267 and DMS-01-04278.Research partially supported by FAPERJ grant E-26/151.905/2000 and CNPq.     

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.     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

Low-temperature broken-symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of spin S-->infinity, there is a zero temperature (T) Lifshitz point at J(3)=1/4J(1), with long-range spiral spin order at T=0 for J3>1/4J(1). We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0< or =T相似文献   

An Ultimate Frustration in Classical Lattice-Gas Models

A classical lattice-gas model is called frustrated if not all of its interactions can attain their minima simultaneously. The antiferromagnetic Ising model on the triangular lattice is a standard example.^{(1, 29)} However, in all such models known so far, one could always find nonfrustrated interactions having the same ground-state configurations. Here we constructed a family of classical lattice-gas models with finite-range, translation-invariant, frustrated interactions and with unique ground-state measures which are not unique ground-state measures of any finite-range, translation-invariant, nonfrustrated interactions.Our ground-state configurations are two-dimensional analogs of one-dimensional, most homogeneous,⁽¹³⁾ nonperiodic ground-state configurations of infinite-range, convex, repulsive interactions in models with devil's staircases.Our models are microscopic (toy) models of quasicrystals which cannot be stabilized by matching rules alone; competing interactions are necessary.     

Lattice dynamical study of alkali metals: An unified approach based on CGW model

The phonon dispersion relations for lithium, sodium, potassium, rubidium and cesium along the principal symmetry directions as well as their lattice specific heats have been deduced using Clark, Gazis and Wallis angular force model. This model which conforms to the translational symmetry of the lattice, reproduces the observed crossover in lithium along [ζ00] direction at ζ = 0·49, without producing any crossovers in other alkali metals. Besides, the theoretical dispersion curves of all alkali metals are in excellent agreement with the corresponding experimental or homologous dispersion relations and theirϑ _D values compare well with the experimental values over a wide temperature range. It is shown that the strength of electron-ion interactions plays a significant role in the success of any unified lattice dynamical study of alkali metals while the three-body interactions of thecgw model do not. The importance of umklapp processes, failure of the earlier models to produce a crossover and the experimentalϑ _D-T curve in lithium as well as the apparent variation in the nature and range of atomic interactions of alkali metals are discussed.     

An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order ²⁵ the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through ²³ for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S = 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 5, .     

Evidence for a valence transition in UxY1-xSb

Electrical, optical and lattice-constant measurements on single crystalline U_xY_1-xSb (x=0, 0.01, 0.03, 0.08, 0.15, 0.20, 0.30, 0.70 and 1) reveal a nonmagnetic U 5f² singlet groundstate for x ? 0.15, a lowering of the f³→f²d¹ transition energy with decreasing x for x > 0.15 and a marked anomaly of the lattice parameter for x ? 0.15. These results as well as the anomalous concentration dependence of the U moment can be described by a valence transition of U at a concentration of about 15% U (x = 0.15).     

Consequences of Xe–H Cross Relaxation in Aqueous Solutions

We have investigated the transfer of polarization from ¹²⁹Xe to solute protons in aqueous solutions to determine the feasibility of using hyperpolarized xenon to enhance ¹H sensitivity in aqueous systems at or near room temperatures. Several solutes, each of different molecular weight, were dissolved in deuterium oxide and although large xenon polarizations were created, no significant proton signal enhancement was detected in -tyrosine, α-cyclodextrin, β-cyclodextrin, apomyoglobin, or myoglobin. Solute-induced enhancement of the ¹²⁹Xe spin–lattice relaxation rate was observed and depended on the size and structure of the solute molecule. The significant increase of the apparent spin–lattice relaxation rate of the solution phase ¹²⁹Xe by α-cyclodextrin and apomyoglobin indicates efficient cross relaxation. The slow relaxation of xenon in β-cyclodextrin and -tyrosine indicates weak coupling and inefficient cross relaxation. Despite the apparent cross-relaxation effects, all attempts to detect the proton enhancement directly were unsuccessful. Spin–lattice relaxation rates were also measured for Boltzmann ¹²⁹Xe in myoglobin. The cross-relaxation rates were determined from changes in ¹²⁹Xe relaxation rates in the α-cyclodextrin and myoglobin solutions. These cross-relaxation rates were then used to model ¹H signal gains for a range of ¹²⁹Xe to ¹H spin population ratios. These models suggest that in spite of very large ¹²⁹Xe polarizations, the ¹H gains will be less than 10% and often substantially smaller. In particular, dramatic ¹H signal enhancements in lung tissue signals are unlikely.     

Real space renormalization group with effective interactions: applications to 2-D spin lattices

The Blochs theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The J ₂/J ₁ checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed.Received: 11 June 2004, Published online: 30 September 2004PACS: 71.10.-W Theories and models of many-electron systems - 71.15.Nc Total energy and cohesive energy calculations - 75.10.-b General theory and models of magnetic ordering     

New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈s〉=〈αs〉=0) and the correlated ordered (〈s〉 ≠0 and 〈α〉=〈s〉=0) states.     

The O(n) Loop Model on the 3–12 Lattice

The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3–12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related via a simple transformation of variables. When n = 0 this gives the recently found exact value = 1.711041... for the connective constant of self-avoiding walks on the 3–12 lattice. The exact critical points are recovered for the Ising model on the 3–12 lattice and the dual asanoha lattice at n = 1.     

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei

competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0~+ and 1~+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.     

The low-lying mass spectrum of the N = 1 SU(2) SUSY Yang-Mills theory with Wilson fermions

We analyze the low energy spectrum of bound states of the N = 1 SU(2) SUSY Yang-Mills Theory (SYM). This work continues the investigation of the non-perturbative properties of SYM by Monte Carlo simulations in the Wilson discretization with dynamical gluinos. The dynamics of the gluinos is included by the Two-Step Multi-Bosonic Algorithm (TSMB) for dynamical fermions. A new set of configurations has been generated on a lattice at and . The analysis also includes sets of configurations previously generated on a smaller ( ) lattice at and 0.1955. Guided by predictions from low energy Lagrangians, we consider spin-1/2, scalar and pseudoscalar particles. The spectrum of SYM is a challenging subject of investigation because of the extremely noisy correlators. In particular, meson-like correlators contain disconnected contributions. The larger time-extension of the lattice allows to observe two-state signals in the effective mass. Finite-volume effects are monitored by comparing results from the two lattice sizes.Received: 14 September 2004, Revised: 29 October 2004, Published online: 21 December 2004     

Canonical local algorithms for spin systems: heat bath and Hasting’s methods

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising 1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising 1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the continuous Ising model (N = 1), the Ising model (N = 1), the XY model (N = 2), the Heisenberg model (N = 3), the Heisenberg model (N = 3), the O(4) model with applications to the SU(2) lattice gauge theory, and the general O(N) vector spins with .Received: 16 August 2004, Published online: 21 October 2004PACS: 05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models - 75.10.Nr Spin-glass and other random models     

C掺杂金红石相TiO2的电子结构和光学性质的第一性原理研究

运用第一性原理的局域密度近似+U(0 ≤U≤9 eV)方法研究了本征金红石相TiO₂在不同U值(对Ti-3d电子)下的禁带宽度、晶体结构以及不同比例C元素掺杂的金红石相TiO₂的电子结构和光学性质, 研究表明, TiO₂的禁带宽度和晶格常数随着U值的增加而增大. 综合考虑取U=3 eV并对其计算结果进行修正. 对于掺杂体系, 发现C 元素的掺杂在金红石相TiO₂中引入杂质能级, 杂质能级主要由O-2p轨道和C-2p轨道耦合形成, 杂质能级的引入可以增加TiO₂对可见光的响应, 从而使TiO₂的吸收范围增大. C原子掺杂最佳比例为8.3%, 此时光学吸收边的红移程度最明显, 可增大光吸收效率, 从而提高了TiO₂光催化效率.     

Hadron spectrum in a Euclidean invariant regularization of QCD at strong coupling

A new random lattice regularization, which preserves exact euclidean invariance, is proposed for QCD. The corresponding action couples any two points on the random lattice with a gaussian damping of range b in the euclidean distance of the points. This property, which avoids the introduction of the concept of nearest neighbours on a random lattice, greatly simplifies computations of physical observables with respect to the situation of the standard random lattice models. The present calculation of the hadron spectrum of a SU(N = 3) gauge model is performed at strong coupling β = 0, at leading order in 1/N and in the inverse lattice point density ?. The results for mesons of definite spin-parity and flavor are quite good; the results for the baryons are, as usual, less satisfying (small N-Δ mass difference), but are also expected to be less reliable in our approximations. The problem of the regularization of chiral fermions is not settled in this paper where the used approximations yield a massless η-boson.