New phase in a spin-1/2 Falicov-Kimball model

In this investigation we present exact results on the spin-1/2 Falicov-Kimball model. We obtain ground-state results for arbitrary dimensions using the method of in-equalities as well as results on the thermodynamics for large dimensions. As a new feature (not possible in a spinless model) we obtain a transition (which may be discontinuous) into a new state with a high density of pairs of thef-electrons.Supported in part by the Deutsche Forschungsgemeinschaft     

Existence of a phase transition in a spin-1/2 Falicov-Kimball model

In this paper we present a proof for the existence of a phase transition in the symmetric case of the spin-1/2 Falicov-Kimball model in more than one dimension. For a certain regime of the parameters of this model we are able to show, that the superstructure of the localizedf-electrons in the ground-state, which has been investigated and published some time ago, persists in part up to small nonzero temperatures.Supported in part by the Deutsche Forschungsgemeinschaft     

Some exact results for the three-layer zamolodchikov model

In this talk, we present our recent results on the three-layer Zamolodchikov model. We discuss solutions to the Bethe ansatz equations following from functional relations. We consider two regimes I and II that differ by the signs of the spherical sides (a₁, a₂, a₃) → (?a₁, ?a₂, ?a₃). Also, we accept the two-line hypothesis for regime I and the one-line hypothesis for regime II. In the thermodynamic limit, we derive integral equations for distribution densities and solve them exactly. Using this solution, we calculate the partition function for the three-layer Zamolodchikov model and check the compatibility of this result with functional relations. We also discuss the reasons for the discrepancy with Baxter’s result of 1986.     

Asymptotically exact variational approach to the strong coupling Hubbard model

In this contribution we use a generalization of Bogoljubov's variational principle, in order to develop a molecular field theory of the Hubbard model, which becomes asymptotically exact in the strong coupling limit. For this purpose the Hamiltonian is rotated by a unitary two-particle transformation in a way which was previously introduced by Kapustin, before the variational principle is applied.Project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt financed by special funds of the Deutsche Forschungsgemeinschaft.     

Some exact results for the anderson model of an impurity

Summary General formulae for the valence, charge and spin susceptibility, and specific heat at low temperature and zero magnetic field are obtained for the Anderson model of an impurity with the use of the Betheansatz method, following the work of Tsvelick and Wiegmann.

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Riassunto Si ottengono formule generali per la valenza, la carica e suscettibilità di spin e per il calore specifico a temperatura bassa e campo magnetico zero per il modello di Anderson di un'impurità con l'uso del metodo dell'ansatz di Bethe seguendo il lavoro di Tsvelick e Wiegmann.

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Резюме Получаются общие формулы для валентности, заряда, спиновой восприимчивости и удельной теплоемкости при низкой температуре и нулевом магнитном поле для модели Андерсона для описания примеси с использованием подхода Бете.

     

Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

We consider the one-dimensional Hubbard model with infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators.     

Some characteristic behavior of mixed spin-1/2 and spin-1 Ising nano-tube

The magnetization of a cylindrical Ising nano-tube is investigated by the use of the effective field theory with correlations. The effects of the crystal field couplings at the surface shell to the order parameters, susceptibility, internal energy, specific heat and free energy are investigated. Some characteristic phenomena are examined in the thermal variations, depending on crystal field term. Moreover, tricritical and critical points are found on the (D/J,kT/J) plane, where D/J and kT/J are reduced crystal-field and temperature, respectively.     

Ground state properties of the falicov-kimball model in the strong coupling limit

We present some analytic results concerning the ground state of the one-dimensional Falicov-Kimball model in the strong coupling limit. Using the perturbation theory, we find: (i) The well-expected phase segregation takes place for ¦U¦ (U is the interaction strength), (ii) For finiteU there exists the critical value of the interaction strengthU =U _c, below which the segregated phase — an incoherent mixture of the empty and full lattices cannot be the ground state of the model. We give the analytical expression for this boundary. Finally, we discuss the phase diagram of the model for some special configuration of ions.     

Bipartite entanglement in spin-1/2Heisenberg model

The bipartite entanglement of the two-and three-spin Heisenberg model was investigated by using the concept of negativity.It is found that for the ground-state entanglement of the two-spin model,the negativity always decreases as B increases if A Δ＜y-1,and it may keep a steady value of 0.5in the region of B＜J[(Δ+1)2-y2]1/2if Δ＞y-1,while for that of the three-spin model,the negativity exhibits square wave structures if y=0 or Δ=0.For thermal states,there are two areas showing entanglement,namely,the main region and the sub-region.The main region exists only when Δ＞Δc(Δc1=and(y2-1)/2for the 2-and 3-spin model respectively)and extends in terms of B and T as Δ increases,while the sub-region survives only when y≠0 and shrinks in terms of B and T as Δ increases.     

Bipartite entanglement in spin-1/2 Heisenberg model

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B2－γ²]^1/2 if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.     

Fermion kinetics in the Falicov-Kimball limit of the three-band Emery model

The three-band Emery model is reduced to a single-particle quantum model of Falicov-Kimball type, by allowing only up-spins to hop, and forbidding double occupation by projection. It is used to study the effects of geometric obstruction on mobile fermions in thermodynamic equilibrium. For low hopping overlap, there appears a plateau in the entropy, due to charge correlations, and related to real-space disorder. For large overlap, the equilibrium thermopower susceptibility remains anomalous, with a sign opposite to the one predicted from the single-particle density of states. The heat capacity and non-Fermi liquid response are discussed in the context of similar results in the literature. All results are obtained by evaluation of an effective single-particle free-energy operator in closed form. The method to obtain this operator is described in detail.     

Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling

Magnetoelastic properties of the spin-1/2 Ising-Heisenberg model on doubly decorated planar lattices partially amenable to lattice vibrations are examined within the framework of the harmonic approximation and decoration-iteration transformation. It is shown that the magnetoelastic coupling may lead to a spontaneous distortion of the vibrating decorating atoms and the mutual interplay between quantum spin fluctuations and local lattice deformations enhances typical quantum features like the quantum reduction of the magnetization in the ground state of the quantum antiferromagnetic phase, while it does not affect the ground-state behaviour of the classical ferromagnetic phase. It also turns out that the spontaneous distortion is responsible for a much more pronounced reduction of the critical temperature in the quantum antiferromagnetic phase than in the classical ferromagnetic phase.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Thermodynamics of the two-dimensional spin-1/2 XY model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions. This hierarchy of Ising-like models is studied by means of analytic and Monte Carlo techniques. We demonstrate that the sequence of these Ising models can be used to calculate accurately the thermodynamics of the two-dimensional spin-1/2 XY model. By calculating the specific heat, spin correlation functions, susceptibilities and a disorder parameter, we address the question of the nature of the phase transition in the two-dimensional spin-1/2 XY model.     

The random distribution of the coordination numbers in the mixed spin-1/2 and spin-2 Blume-Capel model

The effects of random distribution of coordination numbers are investigated for the mixed spin-1/2 and spin-2 Blume-Capel model on the Bethe lattice in terms of exact recursion relations. The usual coordination numbers, i.e. $q=3,4$ and 6, corresponding to the honeycomb, square and simple cubic lattices, respectively, are considered. Two different q values are taken as couples and are varied randomly in terms of a standard-random approach on the shells of the Bethe lattice with some probabilities. It is found that the model gives either first- or second-order phase transitions for appropriate values of probability (p) and single ion anisotropy (d). One or two tricritical points are also observed depending on the given values of p and d, respectively.     

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.