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We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is found for arbitrary N. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex distribution functions. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model., Comment: 11 pages, 7 EPS figures included, extended version

Low temperature quantum corrections to the density of states (DOS) and the conductivity are examined for a two-dimensional(2D) square crystal with substitutional impurities. By summing the leading logarithmic corrections to the DOS its energy dependence near half-filling is obtained. It is shown that substitutional impurities do not suppress the van Hove singularity at the middle of the band, however they change its energy dependence strongly. Weak disorder due to substitutional impurities in the three-dimensional simple cubic lattice results in a shallow dip in the center of the band. The calculation of quantum corrections to the conductivity of a 2D lattice shows that the well-known logarithmic localization correction exists for all band fillings. Furthermore the magnitude of the correction increases as half-filling is approached. The evaluation of the obtained analytical results shows evidence for delocalized states in the center of the band of a 2D lattice with substitutional impurities.

A real space diagrammatic method, which is an extension of the Berezinskii technique to problems with periodic boundary condition, is formulated to study the density of states (DOS) \rho(\epsilon,\phi) and its moments for a one-channel weakly disordered ring threaded by an external magnetic flux \phi. The exact result obtained for the average value of the DOS shows that \rho(\epsilon,\phi) oscillates with a period of the flux quantum \phi_0=hc/e. However all higher moments of the DOS oscillate with the halved period \phi_0/2. The exact expression for the DOS is valid for both weak localization (L >> l, where L is the rings circumference and l is the mean free path) and ballistic (L < l) regimes. In the weak localization regime the distribution function of the DOS is calculated, which turns out to be of logarithmic normal form., Comment: 17 pages including figures

The fermionic Ising spin glass is analyzed for arbitrary filling and for all temperatures. A selforganized 3-band structure of the model is obtained in the magnetically ordered phase. Deviation from half filling generates a central nonmagnetic band, which becomes sharply separated at T=0 by (pseudo)gaps from upper and lower magnetic bands. Replica symmetry breaking effects are derived for several observables and correlations. They determine the shape of the 3-band DoS, and, for given chemical potential, influence the fermion filling strongly in the low temperature regime., Comment: 13 pages

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states $\rho(\epsilon,\phi)$ of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of $\rho(\epsilon,\phi)$ with a period of the flux quantum $\phi_0= hc/e $. As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime (L >> l) to the ballistic one (L <= l). The analytical expression for the density of states shows the exact dependence of $\rho(\epsilon,\phi)$ on the ring's circumference and on disorder strength for both regimes., Comment: extended and illustrated version

We report progress in understanding the fermionic Ising spin glass with arbitrary filling. A crossover from a magnetically disordered single band phase via two intermediate bands just below the freezing temperature to a 3-band structure at still lower temperatures - beyond an almost random field instability - is shown to emerge in the magnetic phase. An attempt is made to explain the exact solution in terms of a quantum Parisi phase. A central nonmagnetic band is found and seen to become sharply separated at T=0 by gaps from upper and lower magnetic bands. The gap sizes tend towards zero as the number of replica symmetry breaking steps increases towards infinity. In an extended model, the competition between local pairing superconductivity and spin glass order is discussed., Comment: 3 pages, contribution to "ECRYS-99"

We solve the fermionic version of the Ising spin glass for arbitrary filling \mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from \mu to the anisotropy parameter D, we also obtain the solution of the S=1 Sherrington-Kirkpatrick model. An analytic expression for T=0 gives an improved critical value for the first-order phase transition. We revisit the question of stability against replica-diagonal fluctuations and find that the appearance of complex eigenvalues of the Almeida-Thouless matrix is not an artifact of the replica-symmetric approximation., Comment: 8 pages

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials \mu. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for infinity-step breaking. Suppression of reentrant SG - SC - SG transitions due to RPSB is found and discussed in context of ferromagnet - SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high T_c superconductors. We find a crossover line traversing the SG-phase with (\mu=0,T=0) as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mezard vector replica symmetry breaking to occur at low temperatures beyond., Comment: 24 pages, 14 figures replaced by published version

The phase diagram of a single species fermion model allowing for local pairing superconductivity (SC) and spin glass order (SG) is derived as a function of chemical potential \mu and ratio r=v/J between attractive coupling v and frustrated magnetic interaction J. For ratios larger than a characteristic r_c(\mu), superconductivity does not allow for SG order, while for smaller values a very detailed phase diagram arises with entangled spin glass and superconducting transitions. Our results for the Green's functions show that superconductivity occurring in the magnetic interaction band is of gapless type with a crossover from strongly gapless, within a certain range below T_c, to very weakly gapless in a wide low temperature regime, and hardgapped at T=0., Comment: 4 pages, 5 figures

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagom\'e lattice., Comment: 33 pages, Latex, 9 encapsulated postscript figures, J. Phys. A, in press