1,904 research outputs found
Observables of the generalized 2D Yang-Mills theories on arbitrary surfaces: a path integral approach
Using the path integral method, we calculate the partition function and the
generating functional (of the field strengths) of the generalized 2D Yang-Mills
theories in the Schwinger--Fock gauge. Our calculation is done for arbitrary 2D
orientable, and also nonorientable surfaces.Comment: 6 pages, LaTe
String Theory and Quark Confinement
This article is based on a talk given at the ``Strings'97'' conference. It
discusses the search for the universality class of confining strings. The key
ingredients include the loop equations, the zigzag symmetry, the non-linear
renormalization group. Some new tests for the equivalence between gauge fields
and strings are proposed.Comment: 13 pages, latex; talk at STRINGS'9
Pion Superfluidity and Meson Properties at Finite Isospin Density
We investigate pion superfluidity and its effect on meson properties and
equation of state at finite temperature and isospin and baryon densities in the
frame of standard flavor SU(2) NJL model. In mean field approximation to quarks
and random phase approximation to mesons, the critical isospin chemical
potential for pion superfluidity is exactly the pion mass in the vacuum, and
corresponding to the isospin symmetry spontaneous breaking, there is in the
pion superfluidity phase a Goldstone mode which is the linear combination of
the normal sigma and charged pion modes. We calculate numerically the gap
equations for the chiral and pion condensates, the phase diagrams, the meson
spectra, and the equation of state, and compare them with that obtained in
other effective models. The competitions between pion superfluidity and color
superconductivity at finite baryon density and between pion and kaon
superfluidity at finite strangeness density in flavor SU(3) NJL model are
briefly discussed.Comment: Updated version: (1)typos corrected; (2)an algebra error in Eq.(87)
corrected; (3)Fig.(17) renewed according to Eq.(87). We thank Prof.Masayuki
Matsuzaki for pointing out the error in Eq.(87
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
Difficulties in Inducing a Gauge Theory at Large N
It is argued that the recently proposed Kazakov-Migdal model of induced gauge
theory, at large , involves only the zero area Wilson loops that are
effectively trees in the gauge action induced by the scalars. This retains only
a constant part of the gauge action excluding plaquettes or anything like them
and the gauge variables drop out.Comment: 6 pages, Latex, AZPH-TH/93-01, COLO-HEP/30
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
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
Entanglement renormalization and gauge symmetry
A lattice gauge theory is described by a redundantly large vector space that
is subject to local constraints, and can be regarded as the low energy limit of
an extended lattice model with a local symmetry. We propose a numerical
coarse-graining scheme to produce low energy, effective descriptions of lattice
models with a local symmetry, such that the local symmetry is exactly preserved
during coarse-graining. Our approach results in a variational ansatz for the
ground state(s) and low energy excitations of such models and, by extension, of
lattice gauge theories. This ansatz incorporates the local symmetry in its
structure, and exploits it to obtain a significant reduction of computational
costs. We test the approach in the context of the toric code with a magnetic
field, equivalent to Z2 lattice gauge theory, for lattices with up to 16 x 16
sites (16^2 x 2 = 512 spins) on a torus. We reproduce the well-known ground
state phase diagram of the model, consisting of a deconfined and spin polarized
phases separated by a continuous quantum phase transition, and obtain accurate
estimates of energy gaps, ground state fidelities, Wilson loops, and several
other quantities.Comment: reviewed version as published in PRB; this version includes a new
section about the accuracy of the results several corrections and added
citation
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
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
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