Thermodynamics of the Hubbard model on stacked honeycomb and square lattices

We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling.     

Self-avoiding random walk with multiple site weightings and restrictions

We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight omegal is assigned to each (l+1)-fold visited lattice site, and self-avoidance is incorporated by restricting to a maximal number K of visits to any site via setting omegal=0 for l>or=K. In this Letter we study this model on the square and simple cubic lattices for the case K=3. Moreover, we consider a variant of this model, in which we forbid immediate self-reversal of the random walk. We perform simulations for random walks up to n=1024 steps using FlatPERM, a flat histogram stochastic growth algorithm. We find evidence that the existence of a collapse transition depends sensitively on the details of the model and has an unexpected dependence on dimension.     

Ordering of body-centered cubic ternary alloys with three types of site. I

The ordering theory of A-B-D alloys with body-centered cubic (bcc) lattices and three types of site is examined by the Gorskii-Bragg-Williams approximation. It is shown that under certain conditions there can be two critical temperatures (T₀) for the order-disorder phase transition. The case of alloys with a quasi-binary BA-BD section is examined in detail.     

Symmetric behavior of vortex states of superconducting networks in a magnetic field

We present magnetic field dependence of phase transition temperature and vortex configuration of superconducting networks based on theoretical study. The applied magnetic field is called “filling field” that is defined by applied magnetic flux (in unit of the flux quantum) per unit loop of the superconducting network. If a superconducting network is composed of very thin wires whose thicknesses are less than coherence length, the de Gennes–Alexander (dGA) theory is applicable. We have already shown that field dependences of transition temperature curves have symmetric behavior about the filling field of 1/2 by solving the dGA equation numerically in square lattices, honeycomb lattices, cubic lattices and those with randomly lack of wires networks. Many experimental studies also show the symmetric behavior. In this paper, we make an explicit theoretical explanation of symmetric behaviors of superconducting network respect to the applied field.     

The Ising model on random lattices in arbitrary dimensions

We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising spins on random surfaces. We show that, in the continuum limit, the spin system does not exhibit a phase transition at finite temperature, in agreement with numerical investigations. Furthermore we outline a general method to study critical behavior in colored tensor models.     

Calculation of mechanical strength of crystalline lattices of iron,molybdenum, and tungsten

Semiempirical tensor equations of state were obtained for iron, molybdenum, and tungsten and used to examine the mechanical properties of their crystalline lattices under conditions of a complex system of stresses. The most hazardous systems of stresses were distinguished, and stresses and deformations were calculated. The obtained values of strength are in good agreement with the existing empirical data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 74–78, 1972.     

Characterizing quantum phase transition by teleportation

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.     

Negative Poisson's ratio materials via isotropic interactions

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.     

Metal-insulator transition in the Hubbard model with incommensurate magnetic structures

The metal-insulator transition for the square, simple cubic, and body centered cubic lattices has been studied within the Hubbard model at half-filling taking into account nearest- and next-nearest-neighbor electron hopping. Both staggered antiferromagnetic and incommensurate magnetic states (spin-spiral wave) have been considered. The inclusion of the latter states for the three-dimensional lattices does not change the general pattern of the metal-insulator transition, but opens the fundamentally new possibility of the metal-insulator transition of the first order between the magnetically ordered states for the square lattice.     

Convection in chemical fronts with quadratic and cubic autocatalysis

Convection in chemical fronts enhances the speed and determines the curvature of the front. Convection is due to density gradients across the front. Fronts propagating in narrow vertical tubes do not exhibit convection, while convection develops in tubes of larger diameter. The transition to convection is determined not only by the tube diameter, but also by the type of chemical reaction. We determine the transition to convection for chemical fronts with quadratic and cubic autocatalysis. We show that quadratic fronts are more stable to convection than cubic fronts. We compare these results to a thin front approximation based on an eikonal relation. In contrast to the thin front approximation, reaction-diffusion models show a transition to convection that depends on the ratio between the kinematic viscosity and the molecular diffusivity. (c) 2002 American Institute of Physics.     

Structure,properties, and possible mechanisms of formation of diamond-like phases

An analysis was performed for relations between the structural parameters and the properties of 36 carbon diamond-like phases consisting of atoms occupying crystallographically equivalent positions. It was found that the crystal lattices of these phases were in stressed states with respect to the cubic diamond lattice. The density of diamond-like phases, their sublimation energies, bulk moduli, hardnesses, and band gaps depend on the deformation parameters Def and Str. The most stable phases must be phases with minimal parameters Def and Str and also with ring parameter Rng that is most close to the corresponding parameter of cubic diamond. The structures and energy characteristics of fullerites, nanotube bundles, and graphene layers of which diamond-like phases can be obtained as a result of polymerization at high pressures have been calculated.     

Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model with second-order field equations

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.     

Simultaneous analysis of three-dimensional percolation models

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 2013, 87（5）： 052107], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold Pc, and thus provide a powerful means for determining Pc. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of Pc are obtained.     

Anti-ferroelectric polarization transitions in quantum-dot-quantum-well arrays

With the improvement in fabrication techniques it is now possible to produce atom-like semiconductor structures with unique electronic properties. This makes possible periodic arrays of nanostructures in which the Coulomb interaction, polarizability and tunneling may all be varied. This theoretical study investigates the collective properties of 2D arrays and 3D face-centered cubic lattices of singly charged nanospherical shells, sometimes called 'quantum dot-quantum wells' or 'core-shell quantum dots'. We find that, for square arrays, the classical ground state is an Ising anti-ferroelectric (AFE), while the quantum ground state undergoes a transition from a uniform state to an AFE. The triangular lattice, in contrast, displays properties characteristic of frustration. Three-dimensional face-centered cubic lattices polarize in planes, with each layer alternating in direction. We discuss the possible experimental signals of these transitions.     

Single crystal and powder EPR study of trivalent gadolinium in Cs2NaBiCl6 in the 30-300 K interval

A crystalline electric field cubic symmetry site has been reported for Gd³⁺ in Cs₂NaBiCl₆ at room temperature. This host exhibits an apparent structural transformation below 100 K that is completely reversible. However, an EPR examination for a powdered sample of Cs₂NaBiCl₆:Gd³⁺ clearly demonstrates that there are no new large crystalline electric field symmetry sites arising between the transition temperature (100 K) and 30 K, suggesting, therefore, that the site symmetry remains predominantly cubic even at temperatures close to 30 K. In order to substantiate this statement, a computer EPR powder simulation was performed using the single-crystal-spin-Hamiltonian parameters obtained from the three different sites that emerge from the original site while observed at 30 K. A remarkable agreement is observed while comparing the computer-simulated data with that of powdered experimental data. It is important to mention here that several attempts were done trying to fit the observed new spectra to lower crystalline field symmetries, however, our best analytical adjustment was obtained with the cubic spin-Hamiltonian.Below 30 K, new structural transitions are present and the lattice loses its original cubic nature. However, at 10 K the EPR spectrum of the crystal again shows only seven lines that are very broad. This new spectrum cannot be fitted with previously used cubic spin-Hamiltonian parameters.     

Phase transitions at high pressure in tetracyanoethylene

We report in situ x-ray diffraction studies in tetracyanoethylene (TCNE) at high pressure using diamond anvil cell (DAC) at Elettra synchrotron source, Trieste, Italy. Experiments were performed with both the polymorphic phases (monoclinic and cubic) of TCNE as the starting phase. While starting with monoclinic (the high temperature stable) TCNE, it was found that the Bragg peaks get broadened with increase of pressure and above 5 GPa only few broad peaks remained to be observed. On release of pressure from 6.4 GPa, when the sample started turning black, the diffraction pattern at ambient pressure corresponds to cubic, the other crystalline phase of TCNE. Results reconfirm the monoclinic to cubic transition at high pressure but via an intermediate ‘disordered’ phase. This settles a number of conflicting issues. TCNE represents only system, which undergoes transition from one crystalline to another crystalline phase via a ‘disordered’ metastable phase at high pressure. When the starting phase was cubic (the low temperature stable) no apparent phase transition was observed up to 10.8 GPa.     

Motion decomposition,frame-indifferent derivatives,and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Widespread approaches to generalizing geometrically linear constitutive relations to the case of large displacement gradients have been considered. These approaches are based on the replacement of the material derivatives of stress and strain tensors by frame-indifferent corotational or convective derivatives. The correctness of choosing the indifferent derivatives is analyzed from a more general viewpoint of motion decomposition into rigid and strain-induced motion. It is shown that the use of the Zaremba-Jaumann derivative in constitutive relations corresponds to motion decomposition by the Cauchy-Helmholtz theorem according to which instantaneous rigid rotation of a material particle with small neighborhood is described by the vorticity tensor. The relations derived with the use of the so-called "logarithmic spin" are analyzed. It is noted that the spin tensors entering into these relations are not associated with the material fibers (in particular with the symmetry axes of anisotropic materials) during the entire studied process of deformation. Hence these spins do not describe the rotation of the reference frame (crystallographic one for metals) in which the material property tensor is defined. A new method of motion decomposition is proposed on the basis of a two-level (macro and meso) approach for single and polycrystalline metals. The mesoscopic spin is determined by the rotation rate of the corotational coordinate system associated with the crystallographic direction and crystallographic plane. Mesoscopic constitutive relations are formulated using the proposed spin. The spin of a representative macrovolume is determined by averaging the spins of the crystallites contained in this volume. This spin is used to formulate rate-type elastic constitutive equations. Examples are given to illustrate the stress state determination for loading along closed strain paths and two-segment paths for isotropic and anisotropic (with cubic symmetry, hcp) elastic materials, and an elastoviscoplastic fcc crystallite. The determination is carried out by using the corotational derivatives in the constitutive relations which are obtained by different motion decomposition methods.     

Dynamics of structural transformations between lamellar and inverse bicontinuous cubic lyotropic phases

The liquid crystalline lamellar (L(alpha)) to double-diamond inverse bicontinuous cubic (Q(D)(pi)) phase transition for the amphiphile monoelaidin in excess water exhibits a remarkable sequence of structural transformations for pressure or temperature jumps. Our data imply that the transition dynamics depends on a coupling between changes in molecular shape and the geometrical and topological constraints of domain size. We propose a qualitative model for this coupling based on theories of membrane fusion via stalks and existing knowledge of the structure and energetics of bicontinuous cubic phases.     

Ising models,julia sets,and similarity of the maximal entropy measures

We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.