1,759 research outputs found
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 -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
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
New technique for replica symmetry breaking with application to the SK-model at and near T=0
We describe a novel method which allows the treatment of high orders of
replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly,
without a need for approximations or scaling assumptions. It yields the low
temperature order function q(a,T) in the full range and is
complete in the sense that all observables can be calculated from it. The
behavior of some observables and the finite RSB theory itself is analyzed as
one approaches continuous RSB. The validity and applicability of the
traditional continuous formulation is then scrutinized and a new continuous RSB
formulation is proposed
Nonanalytic quantum oscillator image of complete replica symmetry breaking
We describe the effect of replica symmetry breaking in the field distribution
function P(h) of the T=0 SK-model as the difference between a split Gaussian
and the first excited state of a weakly anharmonic oscillator with
nonanalytic shift by means of the analogy . New numerical
calculations of the leading 100 orders of replica symmetry breaking (RSB) were
performed in order to obtain P(h), employing the exact mapping between density
of states of the fermionic SK-model and P(h) of the standard model,
as derived by Perez-Castillo and Sherrington. Fast convergence towards a fixed
point function for infinite steps of RSB is observed. A surprisingly
small number of harmonic oscillator wave-functions suffices to represent this
fixed point function. This allows to determine an anharmonic potential V(x)
with nonanalytic shift, whose first excited state represents and
hence P(h). The harmonic potential with unconventional shift yields already a very good approximation, since
anharmonic couplings of decay rapidly with
increasing m. We compare the pseudogap-forming effect of replica symmetry
breaking, hosted by the fermionic SK-model, with the analogous effect in the
Coulomb glass as designed by Davies-Lee-Rice and described by M\"uller-Pankov.Comment: 11 pages, 3 figures, submitted to Phil. Mag., special edition in
honour of David Sherrington's 70th birthda
One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin glass model in a transverse field
The one-step replica symmetry breaking (RSB) is used to study a
two-sublattice fermionic infinite-range Ising spin glass (SG) model in a
transverse field . The problem is formulated in a Grassmann path
integral formalism within the static approximation. In this model, a parallel
magnetic field breaks the symmetry of the sublattices. It destroys the
antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase
(SG+AF) characterizing an asymmetric RSB region. In this region,
intra-sublattice disordered interactions increase the difference between
the RSB solutions of each sublattice. The freezing temperature shows a higher
increase with when enhances. A discontinue phase transition from the
replica symmetry (RS) solution to the RSB solution can appear with the presence
of an intra-sublattice ferromagnetic average coupling. The field
introduces a quantum spin flip mechanism that suppresses the magnetic orders
leading them to quantum critical points. Results suggest that the quantum
effects are not able to restore the RS solution. However, in the asymmetric RSB
region, can produce a stable RS solution at any finite temperature for
a particular sublattice while the other sublattice still presents RSB solution
for the special case in which only the intra-sublattice spins couple with
disordered interactions.Comment: 11 pages, 8 figures, accepted for publication in Phys. Rev.
Double Criticality of the Sherrington-Kirkpatrick Model at T=0
Numerical results up to 42nd order of replica symmetry breaking (RSB) are
used to predict the singular structure of the SK spin glass at T=0. We confirm
predominant single parameter scaling and derive corrections for the T=0 order
function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and
a=\infty are shown to be two critical points for \infty-RSB, associated with
two discrete spectra of Parisi block size ratios, attached to a continuous
spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are
obtained with unprecedented accuracy.Comment: 4 pages, 5 figure
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 tricritical
point of metallic quantum spin glasses are derived.Comment: 4 pages, 1 Postscript figure, minor change
Iteratively reweighted compressive sensing based algorithm for spectrum cartography in cognitive radio networks
© 2014 IEEE. Spectrum cartography is the process of constructing a map showing Radio Frequency signal strength over a finite geographical area. In our previous work we formulated spectrum cartography as a compressive sensing problem and we illustrated how cartography can be used in the context of discovering spectrum holes in space that can be exploited locally in cognitive radio networks. This paper investigates the performance of compressive sensing based approach to cartography in a fading environment where realtime channel estimation is not feasible. To accommodate for lack of channel information we take an iterative approach. We extend the well-known iteratively reweighted ℓ1 minimisation approach by exploiting spatial correlation between two points in space. We evaluate the performance in an urban environment where Rayleigh fading is prominent. Our numerical results show a significant improvement in the probability of accurately making a spectrum sensing decision, in comparison to the well-known weighted approach and the traditional compressive sensing based method
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