The one-dimensional XXZ model (s=1/2) in a transverse field, with uniform longrange interactions among the transverse components of the spins, is studied. The model is exactly solved by introducing the Jordan-Wigner transformation and the integral Gaussian transformation. The complete critical behaviour and the critical surface for the quantum and classical transitions, in the space generated by the transverse field and the interaction parameters, are presented. The crossover lines for the various classical/quantum regimes are also determined exactly. It is shown that, besides the tricritical point associated with the classical transition, there are also two quantum critical points: a bicritical point where the classical second-order critical line meets the quantum critical line, and a first-order transition point at zero field. It is also shown that the phase diagram for the first-order classical/quantum transitions presents the same structure as for the second-order classical/quantum transitions. The critical classical and quantum exponents are determined, and the internal energy, the specific heat and the isothermal susceptibility,χ zz T , are presented for the different critical regimes. The two-spin static and dynamic correlation functions, < S z j S z l >, are also presented, and the dynamic susceptibility, χ zz q (ω),is obtained in closed form. Explicit results are presented at T = 0, and it is shown that the isothermal susceptibility, χ zz T , is different from the static one, χ zz q (0). Finally, it is shown that, at T = 0, the internal energy close to the first-order quantum transition satisfies the scaling form recently proposed by Continentino and Ferreira.

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Tight-binding Hamiltonians with single and multiple orbitals exhibit an intriguing array of magnetic phase transitions. In most cases the spin ordered phases are insulating, while the disordered phases may be either metallic or insulating. In this paper we report a Determinant Quantum Monte Carlo study of interacting electrons in a geometry which can be regarded as a two-dimensional Periodic Anderson Model with depleted interacting (f ) orbitals. For a single depletion, we observe an enhancement of antiferromagnetic correlations and formation of localized states. For half of the f -orbitals regularly depleted, the system exhibits a ferrimagnetic ground state. We obtain a quantitative determination of the nature of magnetic order, which we discuss in the context of Tsunetsugu's theorem, and show that, although the dc conductivity indicates insulating behavior at half-filling, the compressibility remains finite.

With the purpose of investigating coexistence between magnetic order and superconductivity, we consider a model in which conduction electrons interact with each other, via an attractive Hubbard on-site coupling U, and with local moments on every site, via a Kondo-like coupling, J. The model is solved on a simple cubic lattice through a Hartree-Fock approximation, within a 'semi-classical' framework which allows spiral magnetic modes to be stabilized. For a fixed electronic density, n , the small J region of the ground state (T  =  0) phase diagram displays spiral antiferromagnetic (SAFM) states for small U. Upon increasing U, a state with coexistence between superconductivity (SC) and SAFM sets in; further increase in U turns the spiral mode into a Néel antiferromagnet. The large J region is a (singlet) Kondo phase. At finite temperatures, and in the region of coexistence, thermal fluctuations suppress the different ordered phases in succession: the SAFM phase at lower temperatures and SC at higher temperatures; also, reentrant behaviour is found to be induced by temperature. Our results provide a qualitative description of the competition between local moment magnetism and superconductivity in the borocarbides family.

The static and dynamic properties of the anisotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N cells with n different exchange interactions and magnetic moments, in a transverse field h, are determined exactly at arbitrary temperatures.