The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges. PACS numbers: 71.27.+a, 75.10.Lp, 75.30.Kz More than 30 years ago, the Hubbard model was introduced to describe band magnetism in transition metals, in particular the ferromagnets Fe, Co and Ni [1][2][3]. However, for a long time it appeared to be a generic model rather for anti-ferromagnetism than for ferromagnetism. At half filling (one electron per site) on bipartite lattices antiferromagnetism emerges in both weak and strong coupling perturbational approaches and, in particular, antiferromagnetism is tractable by renormalization group methods [4]. By contrast, ferromagnetism is a non-trivial strong coupling phenomenon which cannot be investigated by any standard perturbation theory. In fact, our knowledge on the possibility of ferromagnetism in the Hubbard model is still very limited. Only in a few special cases was the Hubbard model proven to have ferromagnetic order. The first rigorous result showing a fully polarized ground state, the theorem by Nagaoka [5], is only valid for a single hole added to the half filled band in the limit of infinite on-site repulsion. In the limit of low electronic density a saturated ferromagnetic ground state has been found recently in the one dimensional Hubbard model on zigzag chains [6,7]. Further, the existence of a ground state with net polarization has been proven for the half filled band case on bipartite lattices with asymmetry in the number of sites per sublattice [8], and in 'flat-band' systems [9].Due to the development of new numerical algorithms and powerful computers the problem of ferromagnetism in the Hubbard model has recently become accessible to numerical investigations of finite systems, at least in reduced dimensions (d = 1, 2). In the presence of a next nearest neighbor hopping, polarized ground states were found very recently in d = 1 [10] and on square lattices in the case of a van Hove singularity at the Fermi energy [11].The rigorous and numerical results mentioned above show that the stability of ferromagnetism is intimately linked with the structure of the underlying lattice and the kinetic energy (i.e. the hopping) of the electrons. This fact has also been observed by exact variational bounds for the stability of saturated ferromagnetism [12][13][14][15], and within approximative methods [16]. Generally, lattices with closed loops and with frustration of the competing antiferromagnetism (non-bipartite lattices) are expected to support ferromagnetism. Non-bipartite lattices have an asymmetric density of states (DOS) and thus a peak away fro...

We present a detailed, quantitative study of the competition between interactionand disorderinduced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e. , within a dynamical mean-field theory, at half-6lling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and suKciently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e. , an increase of the Neel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed. I. INTHODU CTIONThe investigation of interacting electronic systems is one of the most intriguing, albeit di%cult, subjects in condensed matter physics. The same is true for the study of disordered, non-interacting electrons. In view of the theoretical complexity of the two problems taken separately, it is understandable that their combination, i.e. , the simultaneous presence of randomness and interactions, as found in many real systems (e.g. , doped semiconductors near the metal-insulator transition, high-T, superconducting materials close to T"etc. ), leads to new, fundamental questions to which only few secured answers are known. This is all the more true when the interaction and/or the disorder is strong, since there exist hardly any tractable, and at the same time controlled, theoretical method of investigation in this limit.An important starting point for the investigation of interacting, disordered systems was the field-theoretic approach developed for the treatment of noninteracting electrons, i.e. , the scaling theory of Anderson localization.A generalization of this theory to 6nite interactions by Finkelshtein provided essential new insight. However, the appearance of local magnetic moments in the renormalization group treatment discovered by him and Castellani et al. turned out to be a fundamental obstacle for the study of the metal-insulator transition (MIT) itself.A microscopic origin of this instability towards the formation of localized moments can already be traced within Hartree-Fock theory for the disordered Hubbard model ("Anderson-Hubbard model" ) with ofF-diagonal disorder. ' The results indicate that the above renormalization-group approach, as well as is starting poin...

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough U . Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of U above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view. 71.27.+a,75.10.Lp

A detailed study of the paramagnetic to ferromagnetic phase transition in the one-band Hubbard model in the presence of binary-alloy disorder is presented. The influence of the disorder (with concentrations x and 1-x of the two alloy ions) on the Curie temperature T(c) is found to depend strongly on electron density n. While at high densities, n>x, the disorder always reduces T(c); at low densities, n