R

2000

J. Phys. A: Math. Gen.

We solve the fermionic version of the Ising spin glass for arbitrary filling µ and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from µ 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.

Section: Introduction and Mapping Of The Two Modelsmentioning

confidence: 99%

“…) and e βD = e −βµ + e βµ−βU (5) II. RESULTS AT NONZERO TEMPERATURE It has been known for a long time that the two models under consideration are described by two mean-field parameters, q(x) and the replica-diagonal saddle-point value, Q aa =q (in the notation of the ISG f ).…”

Section: Introduction and Mapping Of The Two Modelsmentioning

confidence: 99%

Replica symmetry breaking solution for the fermionic Ising spin-glass and the Ghatak-Sherrington model

Feldmann

2000

J. Phys. A: Math. Gen.

“…Random interactions can lead to unique and decisive physical properties in all sorts of fermionic quantum spin glasses. The entire class of these systems cannot be exhaustively described on the spin level as the example of effects of complex magnetic order on low energy excitations and transport behaviour showed 6 . In this chapter we provide details on technicalities and on physical results obtained by the use of the elements of this new type of many body theory.…”

Section: Basic Elements and Symmetries Of The Many Body Theorymentioning

confidence: 99%

“…In this chapter we provide details on technicalities and on physical results obtained by the use of the elements of this new type of many body theory. One of the major novelties stems from the necessity to include broken replica permutation symmetry of Parisitype 1-3 in the fermionic many body theory 6,25 . We shall demonstrate that the long-time behaviour of averaged fermion propagators is determined by the highly nontrivial Parisi scheme.…”

Section: Basic Elements and Symmetries Of The Many Body Theorymentioning

confidence: 99%

“…In this paper we emphasize and explore the implementation of Parisi replica permutation symmetry breaking 1-5 in the quantum theory of fermionic systems with random interactions. We present details of the derivation of a many body quantum theory with ultrametric structure 6 and we discuss the results in context of the tricritical phase diagram, which is given in the subsequent paper II. Calculations based on the 4-state per site extension of the standard SK-model provide the framework for detailed information that helps to analyze a variety of more complicated fermionic spin-and charge-glass quantum models.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parisi symmetry of the many-body quantum theory of randomly interacting fermionic systems

Rosenow²

1999

Phys. Rev. B

We show that fermion systems with random interactions lead to strong coupling between glassy order and fermionic correlations, which culminates in the implementation of Parisi replica permutation symmetry breaking (RPSB) in their zero temperature quantum field theories. Precursor effects, setting in below fermionic Almeida-Thouless lines, become stronger as the temperature decreases and play a crucial role for many physical properties within the entire low temperature regime. The Parisi ultrametric structure is shown to determine the dynamic behaviour of fermionic correlations (Green's functions) for large times and for the corresponding low energy excitation spectra, which is predicted to affect transport properties in metallic (and superconducting) spin glasses. Thus we reveal the existence and the detailed form of a number of quantum-dynamical fingerprints of the Parisi scheme. These effects, being strongest as T → 0, are contrasted with the replica-symmetric nature of the critical field theory of quantum spin glass transitions at T = 0, which display only small corrections at low T from replica permutation symmetry breaking (RPSB). RPSB-effects moreover appear to influence the loci of the ground state transitions at O(T 0 ) and hence the phase diagrams. From explicit solutions for arbitrary temperatures we also find a new representation of the zero temperature Green's function. This leads to a map of the fermionic (insulating) spin glass solution to the local limit solution of a Hubbard model with a random repulsive interaction. This map exists at any number of replica symmetry breaking steps K. We obtain the distribution of the Hubbard interaction fluctuation and its dependence on the order of RPSB. A generalized mapping between metallic spin glass and random U Hubbard model is conjectured. We also suggest that the new representation of the Green's function at T = 0 can be used for generalizations to superconductors with spin glass phases. Further generalizations of the fermionic Ising spin glass to models with additional spin and charge quantum-dynamics occurring in metallic spin glasses, or due to Coulomb effects including crossover from 4-state per site to effectively 3-state per site models in the limit of infinite repulsive Hubbard coupling are briefly considered. We compare our spin glass results with recent d = ∞ (clean) Hubbard model analyses, paying particular attention to the common role of the corresponding Onsager reaction fields.

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Binderberger

1994

Annalen der Physik

We solve several low temperature problems of an infinite range metailic spin glass model. A compensation problem of T-0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of J-J,(T= 0). The critical value J,(T= 0) = 3/16pF1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter (Qab), a # b, the diagonal is confirmed as order parameter by the result