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

Pseudogaps and Charge Band in the Parisi Solution of Insulating and Superconducting Electronic Spin Glasses at Arbitrary Fillings

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

How to evaluate ground-state landscapes of disordered systems thermodynamical correctly

Ground states of three-dimensional EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained. Then, by applying ballistic search and T=0 Monte-Carlo simulations, it is ensured that each ground state appears with the same probability. Consequently, the results represent the true T=0 thermodynamic behavior. The distribution P(|q|) of overlaps is evaluated. For increasing size the width of P(|q|) and the fraction of the distribution below q_0=0.5 converge to zero. This indicates that for the infinite system P(|q|) is a delta function, in contrast to previous results. Thus, the ground-state behavior is dominated by few large clusters of similar ground states.Comment: 7 pages revtex, 6 figures, 27 reference

Semi-fermionic representation of SU(N) Hamiltonians

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 versio

Selforganized 3-band structure of the doped fermionic Ising spin glass

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 page

O roli precedensu i pewności prawa w niemieckim prawie prywatnym

The article discusses the role of precedents in the German judicial practice. In the European continental tradition, law enactment is within the legislature, whereas the role of the judiciary is to enforce law. In the continental system, precedent does not constitute a source of law sensu stricto, that is, a formal source of law. In order to guarantee the law utility and, ultimately, the legal certainty, courts interpret legal provisions in a unified manner. It is noteworthy that during the recent years the coherent interpretation of legal provisions and, by the same token, the commitment to law development, have increased. That means that a unified interpretation of law performed by courts may be considered a precedent. In this context, precedents and stare decisis have been replacing the logical interpretation of law in German courts. W artykule poruszono kwestię roli precedensów w niemieckiej praktyce prawniczej. W europejskiej tradycji kontynentalnej stanowienie prawa leży w kompetencji władzy ustawodawczej, podczas gdy władza sądownicza polega na stosowaniu prawa. Precedens w systemie kontynentalnym nie stanowi źródła prawa sensu stricto, czyli formalnego źródła prawa. W systemie tym w celu zapewnienia jednolitości prawa, a ostatecznie – pewności prawa, sądy dokonują jednolitej interpretacji przepisów prawnych. Wskazać należy, że w ostatnich latach wzrosło dokonywanie przez sędziów spójnej interpretacji przepisów i przyczynianie się tym samym do rozwoju prawa. Oznacza to, że jednolita wykładnia dokonywana przez sądy może być traktowana jako precedens. W tym znaczeniu coraz częściej w sądach niemieckich precedens i stare decisis zastępują wykładnię logiczną

The XENON100 exclusion limit without considering Leff as a nuisance parameter

In 2011, the XENON100 experiment has set unprecedented constraints on dark matter-nucleon interactions, excluding dark matter candidates with masses down to 6 GeV if the corresponding cross section is larger than 10^{-39} cm^2. The dependence of the exclusion limit in terms of the scintillation efficiency (Leff) has been debated at length. To overcome possible criticisms XENON100 performed an analysis in which Leff was considered as a nuisance parameter and its uncertainties were profiled out by using a Gaussian likelihood in which the mean value corresponds to the best fit Leff value smoothly extrapolated to zero below 3 keVnr. Although such a method seems fairly robust, it does not account for more extreme types of extrapolation nor does it enable to anticipate on how much the exclusion limit would vary if new data were to support a flat behaviour for Leff below 3 keVnr, for example. Yet, such a question is crucial for light dark matter models which are close to the published XENON100 limit. To answer this issue, we use a maximum Likelihood ratio analysis, as done by the XENON100 collaboration, but do not consider Leff as a nuisance parameter. Instead, Leff is obtained directly from the fits to the data. This enables us to define frequentist confidence intervals by marginalising over Leff.Comment: 10 pages;, 9 figures; references adde