1,456 research outputs found
Mean-Field and Anomalous Behavior on a Small-World Network
We use scaling results to identify the crossover to mean-field behavior of
equilibrium statistical mechanics models on a variant of the small world
network. The results are generalizable to a wide-range of equilibrium systems.
Anomalous scaling is found in the width of the mean-field region, as well as in
the mean-field amplitudes. Finally, we consider non-equilibrium processes.Comment: 4 pages, 0 figures; reference adde
Universality of the single-particle spectra of cuprate superconductors
All the available data for the dispersion and linewidth of the
single-particle spectra above the superconducting gap and the pseudogap in
metallic cuprates for any doping has universal features. The linewidth is
linear in energy below a scale and constant above. The cusp in the
linewidth at mandates, due to causality, a "waterfall", i.e., a
vertical feature in the dispersion. These features are predicted by a recent
microscopic theory. We find that all data can be quantitatively fitted by the
theory with a coupling constant and an upper cutoff at
which vary by less than 50% among the different cuprates and for varying
dopings. The microscopic theory also gives these values to within factors of
O(2).Comment: 4 pages, 4 figures; accepted by Phys. Rev. Let
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled
with the 0^th Potts state was investigated by an exact real-space
renormalization group approach. The model was defined on a family of diamond
hierarchical lattices of several fractal dimensions d_F. On these lattices, the
renormalization group transformations became exact for such a model when a
correlation coupling that singles out the 0^th Potts state was included in the
Hamiltonian. The rich criticality presented by the model with q=3 and d_F=2 was
fully analyzed. Apart from the Potts criticality for the zero field, an
Ising-like phase transition was found whenever the system was submitted to a
strong reverse magnetic field. Unusual characteristics such as cusps and
dimensional reduction were observed on the critical surface.Comment: 8 pages, 6 figures. Accepted to be published in Phys. Rev B (2006
Diquark and Pion Condensation in Random Matrix Models for two-color QCD
We introduce a random matrix model with the symmetries of QCD with two colors
at nonzero isospin and baryon chemical potentials and temperature. We analyze
its phase diagram and find phases with condensation of pion and diquark states
in addition to the phases with spontaneously broken chiral symmetries. In the
limit of small chemical potentials and quark masses, we reproduce the mean
field results obtained from chiral Lagrangians. As in the case of QCD with
three colors, the presence of two chemical potentials breaks the flavor
symmetry and leads to phases that are characterized by different behaviors of
the chiral condensates for each flavor. In particular, the phase diagram we
obtain is similar to QCD with three colors and three flavors of quarks of equal
masses at zero baryon chemical potential and nonzero isospin and strange
chemical potentials. A tricritical point of the superfluid transitions found in
lattice calculations and from an analysis in terms of chiral Lagrangians does
not appear in the random matrix model. Remarkably, at fixed isospin chemical
potential, for the regions outside of the superfluid phases, the phase diagram
in the temperature - baryon chemical potential plane for two colors and three
colors are qualitatively the same.Comment: 19 pages, 7 figures, RevTeX
Renormalization Group Approach to Strong-Coupled Superconductors
We develop an asymptotically exact renormalization group (RG) approach that
treats electron-electron and electron-phonon interactions on equal footing. The
approach allows an unbiased study of the instabilities of Fermi liquids without
the assumption of a broken symmetry. We apply our method to the problem of
strongly coupled superconductors and find the temperature T* below which the
high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We
show that T* is the same as the critical temperature Tc obtained in
Eliashberg's strong coupling theory starting from the low-temperature
superconducting phase. We also show that Migdal's theorem is implicit in our
approach. Finally, our results lead to a novel way to calculate numerically,
from microscopic parameters, the transition temperature of superconductors.Comment: 6 pages, 3 figures, expanded presentation, final versio
Isotope effect on the superfluid density in conventional and high-temperature superconductors
We investigate the isotope effect on the London penetration depth of a
superconductor which measures , the ratio of superfluid density to
effective mass. We use a simplified model of electrons weakly coupled to a
single phonon frequency , but assume that the energy gap
does not have any isotope effect. Nevertheless we find an isotope effect for
which is significant if is sufficiently large that it
becomes comparable to , a regime of interest to high cuprate
superconductors and possibly other families of unconventional superconductors
with relatively high . Our model is too simple to describe the cuprates
and it gives the wrong sign of the isotope effect when compared with
experiment, but it is a proof of principle that the isotope effect exists for
in materials where the pairing gap and is not of phonon origin
and has no isotope effect.Comment: 9 pages, 6 figure
Antibound States and Halo Formation in the Gamow Shell Model
The open quantum system formulation of the nuclear shell model, the so-called
Gamow Shell Model (GSM), is a multi-configurational SM that employs a
single-particle basis given by the Berggren ensemble consisting of Gamow states
and the non-resonant continuum of scattering states. The GSM is of particular
importance for weakly bound/unbound nuclear states where both many-body
correlations and the coupling to decay channels are essential. In this context,
we investigate the role of l=0 antibound (virtual) neutron single-particle
states in the shell model description of loosely bound wave functions, such as
the ground state wave function of a halo nucleus 11Li
Phase Transitions In Two Planar Lattice Models And Topological Defects: A Monte Carlo Study
Monte Carlo simulation has been performed in the planar P(_{2}) and P(_{4})
models to investigate the effects of the suppression of topological defects on
the phase transition exhibited by these models. Suppression of the 1/2-defects
on the square plaquettes in the P(_{2}) model leads to complete elimination of
the phase transition observed in this model. However in the P(_{4}) model, on
suppressing the single 1/2-defects on square plaquettes, the otherwise first
order phase transition changes to a second order one which occurs at a higher
temperature and this is due to presence of large number of 1/2-pair defects
which are left within the square plaquettes. When we suppressed these charges
too, complete elimination of phase transition was observed.Comment: Related work has been presented in 22 nd International Conference on
Statistical Physics, STATPHYS22, IISC Bangalore, Indi
Notes on the Hamiltonian formulation of 3D Yang-Mills theory
Three-dimensional Yang-Mills theory is investigated in the Hamiltonian
formalism based on the Karabali-Nair variable. A new algorithm is developed to
obtain the renormalized Hamiltonian by identifying local counterterms in
Lagrangian with the use of fictitious holomorphic symmetry existing in the
framework with the KN variable. Our algorithm is totally algebraic and enables
one to calculate the ground state wave functional recursively in gauge
potentials. In particular, the Gaussian part thus calculated is shown to
coincide with that obtained by Leigh et al. Higher-order corrections to the
Gaussian part are also discussed.Comment: 26 pages, LaTeX; discussions on IR regulators and local counterterms
improved, references adde
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