Hard-core Model Research Articles

Energy spectrum and phase diagrams of two-sublattice hard-core boson model

The energy spectrum, spectral density and phase diagrams have been obtained for two-sublattice hard-core boson model in frames of random phase approximation approach. Reconstruction of boson spectrum at the change of temperature, chemical potential and energy difference between local positions in sublattices is studied. The phase diagrams illustrating the regions of existence of a normal phase which can be close to Mott-insulator (MI) or charge-density (CDW) phases as well as the phase with the Bose-Einstein condensate (SF phase) are built.

Asymptotic enumeration of independent sets on the Sierpinski gasket

The number of independent sets is equivalent to the partition function of the hard-core lattice gas model with nearest-neighbor exclusion and unit activity. We study the number of independent sets md,b(n) on the generalized Sierpinski gasket SGd,b(n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three for d = 2. Upper and lower bounds for the asymptotic growth constant, defined as ZSGdb = limu(∞ ln md,b (n)/v where v is the number of vertices, on these Sierpinski gaskets are derived in terms of the numbers at a certain stage. The numerical values of these ZSGdb are evaluated with more than a hundred significant figures accurate. We also conjecture upper and lower bounds for the asymptotic growth constant ZSGd2 with general d, and an approximation of ZSGd2 when d is large.

Entropy decay for interacting systems via the Bochner-Bakry-Émery approach

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In particular, we obtain volume-independent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.

Quantum phases of hard-core bosons on two-dimensional lattices with anisotropic dipole-dipole interaction

By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the $y$ direction on the two-dimensional $xy$ plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an $O(N)$ Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.

A new method for generating random fibre distributions for fibre reinforced composites

Abstract This paper presents a new method to generate the random distribution of fibres in the transversal cross-section of fibre reinforced composites with high fibre volume fraction. The algorithm, named random sequential expansion (RSE) algorithm by the authors, is based on the hard-core model, but overcomes the jamming limit of hard-core model and is able to generate random distributions for high values of fibre volume fractions. By adjusting the inter-fibre distance parameters, it can generate microstructures with different fibre volume fractions expediently. Statistical analysis is performed on the generated distributions and a good agreement with the completely spatial random (CSR) pattern is found in all statistics analysed. Finite element analysis (FEA) is conducted to predict the effective properties of the generated microstructures. The predicted properties show reasonable agreement with the experimental results. The present algorithm is simple, highly efficient and provides a useful alternative to generate random numerical models that can be used in micromechanical analysis of composites.

Gutzwiller study of phase diagrams of extended Bose—Hubbard models

Hard-core and soft-core extended Bose-Hubbard models with fixed boson densities are studied by using the Gutzwiller variational wave function. The phase diagram of the softcore model strongly depends on its transfer integral. Specifically, a supersolid phase can be the ground state even below half-filling for a large transfer integral. The density difference between nearest-neighbor sites, which is an order parameter of the supersolid phase, strongly depends on the boson density, especially for a small transfer integral.

Effect of dominant three-body interaction in two-dimensional square lattice

The effect of dominant three-body interaction to hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of quantum Monte Carlo method, it is shown explicitly a ρ = 2/3 solid phase with coexistence of charge-density-wave and bond orders appears due to the presence of the dominant three-body interaction. For strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as decreasing the strength of the three-body interaction, forming a lobe structure in the phase diagram. For weak three-body interactions, superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator.

The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model

We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant.

Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range

A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sand Martin (Riparia riparia) colony11Dataset is attached to the online version. on a vertical sand bank are analysed.

Kohn-Luttinger effect and anomalous pairing in repulsive Fermi-systems at low density (Review Article)

We demonstrate the possibility of triplet p-wave pairing at low electron density a large number of models such as 3D and 2D Fermi-gas models with hard-core repulsion, 3D and 2D Hubbard models, and the Shubin-Vonsovsky model. The critical temperature for p-wave pairing can be considerably higher in the spin-polarized case or even in a two-band situation at low density and can reach experimentally observable values of 1–5 K. We also discuss briefly the d-wave pairing and high-Tc superconductivity with Tc ∼ 100 K which arise in the extended Hubbard model and in the generalized t-J model when close to half-filling.

Effect of dominant three-body interaction to the hard-core boson Hubbard model on a two-dimensional square lattice

The effect of dominant three-body interaction to the hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of the quantum Monte Carlo method, a ρ = 2/3 solid phase is shown explicitly with the coexistence of a charge-density wave and a bond-order wave appearing due to the presence of the dominant three-body interaction. For the strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as the strength of the three-body interaction decreases, forming a lobe structure in the phase diagram. For weak three-body interactions, the superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator. Our results may be realized in cold-atom experiments.

Pair superfluid and supersolid of correlated hard-core bosons on a triangular lattice

We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.

Exact Spin Liquid Ground States of the Quantum Dimer Model on the Square and Honeycomb Lattices

We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized Rokhsar-Kivelson points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacting (1+1)-dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground-state correlations are shown to be short ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramatic even-odd effect depending on the circumference and propose that this can be used as a numerical diagnostic of gapped spin-liquid phases, more generally.

A Study of Particle Size Effect on Biomass Torrefaction and Densification

The particle size effect on torrefaction of pine particles and formation of torrefied pellets has been studied in a thermogravimetric analyzer (TGA) and a tubular fixed bed reactor. The fixed bed reactor was also used to produce torrefied samples for a single-die press unit for the densification test. Both the TGA and fixed bed reactor torrefaction test results showed that the torrefaction rate was affected by the particle size, especially at high temperatures. Although the temperature gradient inside particles smaller than 1 mm is very small during torrefaction, the internal diffusion of generated vapors inside particles imposes an impact on the global torrefaction reaction rate. The hard core or nonshrinkage particle model with a first order torrefaction reaction can predict the reaction data reasonably well, with the data-fitted effective vapor diffusivity coefficient. The densification tests showed that more energy was required to make pellets from larger torrefied particles, while the water uptake an...

Improved mixing condition on the grid for counting and sampling independent sets

The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to λ|I|, for a positive real parameter λ. For large λ, computing the partition function (namely, the normalizing constant which makes the weighting a probability distribution on a finite graph) on graphs of maximum degree Δ ≥ 3, is a well known computationally challenging problem. More concretely, let \({\lambda_c(\mathbb{T}_\Delta)}\) denote the critical value for the so-called uniqueness threshold of the hard-core model on the infinite Δ-regular tree; recent breakthrough results of Weitz (Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 140–149, 2006) and Sly (Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 287–296, 2010) have identified \({\lambda_c(\mathbb{T}_\Delta)}\) as a threshold where the hardness of estimating the above partition function undergoes a computational transition. We focus on the well-studied particular case of the square lattice \({\mathbb{Z}^2}\) , and provide a new lower bound for the uniqueness threshold, in particular taking it well above \({\lambda_c(\mathbb{T}_4)}\) . Our technique refines and builds on the tree of self-avoiding walks approach of Weitz, resulting in a new technical sufficient criterion (of wider applicability) for establishing strong spatial mixing (and hence uniqueness) for the hard-core model. Our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure, improving upon what can be achieved by just using the maximum degree. Applying our technique to \({\mathbb{Z}^2}\) we prove that strong spatial mixing holds for all λ < 2.3882, improving upon the work of Weitz that held for λ < 27/16 = 1.6875. Our results imply a fully-polynomial deterministic approximation algorithm for estimating the partition function, as well as rapid mixing of the associated Glauber dynamics to sample from the hard-core distribution.

Approximating entropy for a class of ℤ2Markov random fields and pressure for a class of functions on ℤ2shifts of finite type

AbstractFor a class of ℤ2Markov Random Fields (MRFs)μ, we show that the sequence of successive differences of entropies of induced MRFs on strips of heightnconverges exponentially fast (inn) to the entropy ofμ. These strip entropies can be computed explicitly whenμis a Gibbs state given by a nearest-neighbor interaction on a strongly irreducible nearest-neighbor ℤ2shift of finite typeX. We state this result in terms of approximations to the (topological) pressures of certain functions on such anX, and we show that these pressures are computable if the values taken on by the functions are computable. Finally, we show that our results apply to the hard core model and Ising model for certain parameter values of the corresponding interactions, as well as to the topological entropy of certain nearest-neighbor ℤ2shifts of finite type, generalizing a result in [R. Pavlov. Approximating the hard square entropy constant with probabilistic methods.Ann. Probab.to appear].

A signature of the quantum phase transition in a hard-core boson model in one dimension

We study quantum phase transitions in a hard-core boson model with nearest-neighbor repulsions in one dimension. As we change the repulsive energy, V, between bosons occupying nearest neighbors, the model exhibits a quantum phase transition from a superfluid (SF) to a charge-density-wave (CDW)-type solid phase at half-filling. By using an exact diagonalization method with a modified Lanczos method, we calculate the ground-state energies up to a precision of O(10−7). From the ground-state energies, we obtain the number of dimers by taking numerical derivatives of the groundstate energies. Because the dissolution of the dimers occurs because of the repulsive energy, V, we find a signature of the quantum phase transition from the behaviors of the correlation energy and those of the number of dimers as a function of V.

Anomalous columnar order of charged colloidal platelets

Monte Carlo computer simulations are carried out for a model system of like-charged colloidal platelets in the isothermal-isobaric ensemble (NpT). The aim is to elucidate the role of electrostatic interactions on the structure of synthetic clay systems at high particle densities. Short-range repulsions between particles are described by a suitable hard-core model representing a discotic particle. This potential is supplemented with an electrostatic potential based on a Yukawa model for the screened Coulombic potential between infinitely thin disklike macro-ions. The particle aspect-ratio and electrostatic parameters were chosen to mimic an aqueous dispersion of thin, like-charged, rigid colloidal platelets at finite salt concentration. An examination of the fluid phase diagram reveals a marked shift in the isotropic-nematic transition compared to the hard cut-sphere reference system. Several statistical functions, such as the pair correlation function for the center-of-mass coordinates and structure factor, are obtained to characterize the structural organization of the platelets phases. At low salinity and high osmotic pressure we observe anomalous hexagonal columnar structures characterized by interpenetrating columns with a typical intercolumnar distance corresponding to about half of that of a regular columnar phase. Increasing the ionic strength leads to the formation of glassy, disordered structures consisting of compact clusters of platelets stacked into finite-sized columns. These so-called "nematic columnar" structures have been recently observed in systems of charge-stabilized gibbsite platelets. Our findings are corroborated by an analysis of the static structure factor from a simple density functional theory.

Exact solutions of a multi-component anyon model with SU(N) invariance

We construct a multi-component interacting hard-core anyons model with SU(N) invariance and obtain the exact solutions of the systems by using the nested algebraic Bethe ansatz method with anyonic grading. We find that the grading parameters enter the Bethe ansatz equations as the gauge potentials, and the magnetic flux-like effects are different in the different rapidity sectors. Our results cover the interacting multi-component bosonic or multi-component fermionic models with SU(N) symmetry. In the system, the effective interactions among each component can be tuned by the grading parameters which do not break the integrability, while the integrability of conventional multi-component bosons or fermions requires that all the interactions are equal. The results will be useful to theories and experiments of the cold atomic systems.

Simulation of two-dimensional many-particle hardcore bosons by using the quantum Monte Carlo method

In this paper, the stochastic series expansion quantum Monte Carlo method is employed to investigate the thermodynamic properties of hardcore Bose-Hubbard model in two-dimensional space. The two-dimensional hardcore Bose-Hubbard model can be mapped into the two-dimensional antiferromagnetic quasi-Heisenberg model under transform of bosonic operators. There is an additional term which is proportional to the total number of sites compared with real Heisenberg model and it is difficult for simulation. Using a nonlocal operator-loop update, it allows one to simulate thousands of sites. Our simulation results show that, first, energy decreases with the increase of density of particles in a range from 0 to 0.5, and finally approaches to a fixed value. Moreover, with the size of square lattice increasing, energy also increases. Second, when we fix the system size, energy and magnetization increase with temperature, but not with of chemical potential. When we increase the system size, energy increases, while, the magnetization decreases. Third, specific heat is independent of chemical potential, but it dramatically increases with temperature and approaches to a peak, then decreases slowly. According to Landau theory of superfluidity, the tends of curve for energy and specific heat fit the research of He II in the Landau two-fluid model. Fourth, different square lattice linear system sizes have a little influence on tiny differences to the reciprocal of uniform susceptibility. There are small fluctuations in a range from 0 to 0.5(J/kB), where J is the coupling energy, kB is the Boltzmann constant, but the reciprocal of uniform susceptibility increases with temperature increasing in a range from 0.5 to 2(J/kB). The tends of curve are similar to those of Kondo effect.