Upper bounds for Ising model correlation functions

A Griffiths correlation inequality for Ising ferromagnets is refined and is used to obtain improved upper bounds for critical temperatures. It is shown that, for non-negative external fields, the mean field magnetization is an upper bound for the magnetization of Ising ferromagnets.On leave (1970–71) from Northwestern University, Evanston, Illinois 60201. Supported at IAS by a grant from the Alfred P. Sloan Foundation.     

Upper bounds for the ground-state energy of the exciton-phonon system

Upper bounds for the ground-state energy of the exciton-phonon system are calculated variationally for all ratios of the polaron radii to the exciton radius, whereby the constituents of the exciton are no longer treated as two independent polarons. The numerical results compare satisfactory with experimental data even for the thallous halides.     

Non-perturbative ground-state of a generalized Hubbard model

A generalized Hubbard model with on-site interactionU, inter-site interactionV, and general correlated hopping is studied using a mapping method. An exact solution of the problem of one hole and one doublyoccupied site moving in a ferromagnetic spin background is obtained. The mapping method used is based on mapping the original many-body problem onto an equivalent tight-binding one with impurities in a higher dimensional space.     

The ground-state energy of the B-B′-U Hubbard model in the static-fluctuation approximation

The ground-state energy of the two-sublattice two-dimensional Hubbard model is calculated in the static-fluctuation approximation with allowance for electron transfer from sites to next-to-nearest neighbor sites. In a specific case, the energy of the one-dimensional Hubbard model is calculated and compared with an exact solution.     

Upper and lower bounds to a correlation function for an Ising model with random interactions

We consider the general Ising model with random interactions Jp. We assume that the probability densities of the random interactions are statistically independent and that the averages of the absolute values of the random interactions, |Jp|, are finite. We then show that a correlation function for the regular Ising model with interactions |Jp| and the same quantity with opposite sign are an upper and a lower bound to the corresponding averaged correlation function of the random Ising model under consideration.     

Upper bounds on correlation decay for one-dimensional long-range spin-glass models

Some recent results on one-dimensional spin-glass models with polynomially decreasing interactions are described.     

Remarks on upper bounds for correlation functions of the Ising ferromagnet

We give a sufficient condition under which a general Ising ferromagnet correlation function 〈σ_R〉 is equal to tanhβJ_R. This lemma allows us to giveI. a new simple proof of the 3rd GKS inequality and to show that the r.h.s. of this inequality is the strongest bound for correlation functions from some class of functional bounds,II. the strongest form of the Thompson “mean field” bound and of the Krinsky and Emery bound,III. a generalization of a Krinsky inequality, what results in a good estimation of the pair correlation function in the Ising model.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Upper bounds on the critical temperature for the two-dimensional Blume-Emery-Griffiths model

We obtain rigorous upper bounds for the critical temperature associated with second-order phase transitions of the two-dimensional spin-1 BEG model for real values ofK andD coupling constants and forJ0. We use some correlation equalities and inequalities to show the exponential decay of the two-point function characterizing the disordered phase.     

Dynamic response functions of Hubbard model in Gutzwiller approximation

We calculate the two-point dynamic response functions of the Hubbard model at any filling from a slave-boson representation in the paramagnetic saddle point approximation. We use a spin-rotation invariant form of the representation due to Kotliar and Ruckenstein, for which the saddle point corresponds to Gutzwiller's variational approximation. In addition to the spin and charge susceptibilities, which have the familiar RPA form in the limit of small wavevectorq, the double and single-occupancy response functions are here calculated for the first time.Work partially performed at Department of Physics, University of Florida, Gainesville, FL 32611, USA     

Local approach study of electron correlation effects in the Hubbard model

A variational method which corrects the one-electron ground state locally is applied to study electron correlation effects in the Hubbard model. A two-site cluster approximation is used to calculate the ground state energy functional. For the linear chain and for number of electrons per site up to 0.6, the approximation yields more than 80% of the exact results of Lieb and Wu for the ground state energy. Results for higher dimensional systems are also presented.     

Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration t^′/t could change the wave vector of maximum spin correlation along(π,π) → (π, 5π/6) → (5π/6, 5π/6) → (2π/3, 2π/3),indicating the frustration’s remarkable effect on the magnetism. In the studied filling region ?n? = 1.0 ? 1.3, the doping behaves like some kinds of frustration, which destroys the (π,π) AFM correlation quickly and push the magnetic order to a wide range of the (2π/3, 2π/3)120^° order when the t^′/t is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.