Dynamical CPA approach to an itinerant fermionic spin glass model

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.Comment: 9 pages, 6 figures, revised versio

Random Magnetic Interactions and Spin Glass Order Competing with Superconductivity: Interference of the Quantum Parisi Phase

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 versio