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.