Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.Comment: 39 pages; corrected the lists appearing in Cor. 1.6 and minor changes throughou

Dynamical solutions of a quantum Heisenberg spin glass model

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature $T_c$ of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of $T_c$ by 2% compared to the result obtained in the spin-static approximation. The specific heat $C(T)$ exhibits a pronounced cusp at $T_c$. Contradictory to other reports we do not observe a maximum in the $C(T)$-curve above $T_c$.Comment: 8 pages, 7 figure

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

Tricritical behaviour of Ising spin glasses with charge fluctuations

We show that tricritical points displaying unusal behaviour exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new $T=0$ tricritical point of metallic quantum spin glasses are derived.Comment: 4 pages, 1 Postscript figure, minor change

Field Theory of Mesoscopic Fluctuations in Superconductor/Normal-Metal Systems

Thermodynamic and transport properties of normal disordered conductors are strongly influenced by the proximity of a superconductor. A cooperation between mesoscopic coherence and Andreev scattering of particles from the superconductor generates new types of interference phenomena. We introduce a field theoretic approach capable of exploring both averaged properties and mesoscopic fluctuations of superconductor/normal-metal systems. As an example the method is applied to the study of the level statistics of a SNS-junction.Comment: 4 pages, REVTEX, two eps-figures included; submitted to JETP letter

Random Matrix Theory of a Chaotic Andreev Quantum Dot

A new universality class distinct from the standard Wigner-Dyson ones is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field effectively vanish on average. A random-matrix description of the spectral and transport properties of such a quantum dot is proposed. The weak-localization correction to the tunnel conductance is nonzero and results from the depletion of the density of states due to the coupling with the superconductor. Semiclassically, the depletion is caused by a a mode of phase-coherent long-range propagation of electrons and holes.Comment: minor changes, 4 REVTeX page

Metallic spin glasses

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite temperature phase diagram is described and crossover functions are computed in mean field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.Comment: Contribution to the Proceedings of the ITP Santa Barbara conference on Non-Fermi liquids, 25 pages, requires IOP style file