11,092 research outputs found
A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case
We propose a thermodynamic version of the Axelrod model of social influence.
In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled
Potts model with a bonding interaction that increases with the site matching
traits. We analytically calculate thermodynamic and critical properties for a
1D system and show that an order-disorder phase transition only occurs at T = 0
independent of the number of cultural traits q and features F. The 1D
thermodynamic Axelrod model belongs to the same universality class of the Ising
and Potts models, notwithstanding the increase of the internal dimension of the
local degree of freedom and the state-dependent bonding interaction. We suggest
a unifying proposal to compare exponents across different discrete 1D models.
The comparison with our Hamiltonian description reveals that in the
thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise
behaves like an ordinary thermodynamic 1D interacting particle system.Comment: 19 pages, 5 figure
Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths
We study quantum interference effects on the transition strength for strongly
localized electrons hopping on 2D square and 3D cubic lattices in the presence
of a magnetic field B. These effects arise from the interference between phase
factors associated with different electron paths connecting two distinct sites.
For electrons confined on a square lattice, with and without disorder, we
obtain closed-form expressions for the tunneling probability, which determines
the conductivity, between two arbitrary sites by exactly summing the
corresponding phase factors of all forward-scattering paths connecting them. An
analytic field-dependent expression, valid in any dimension, for the
magnetoconductance (MC) is derived. A positive MC is clearly observed when
turning on the magnetic field. In 2D, when the strength of B reaches a certain
value, which is inversely proportional to twice the hopping length, the MC is
increased by a factor of two compared to that at zero field. We also
investigate transport on the much less-studied and experimentally important 3D
cubic lattice case, where it is shown how the interference patterns and the
small-field behavior of the MC vary according to the orientation of B. The
effect on the low-flux MC due to the randomness of the angles between the
hopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include
Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping
We investigate the magneto-conductance (MC) anisotropy in the variable range
hopping regime, caused by quantum interference effects in three dimensions.
When no spin-orbit scattering is included, there is an increase in the
localization length (as in two dimensions), producing a large positive MC. By
contrast, with spin-orbit scattering present, there is no change in the
localization length, and only a small increase in the overall tunneling
amplitude. The numerical data for small magnetic fields , and hopping
lengths , can be collapsed by using scaling variables , and
in the perpendicular and parallel field orientations
respectively. This is in agreement with the flux through a `cigar'--shaped
region with a diffusive transverse dimension proportional to . If a
single hop dominates the conductivity of the sample, this leads to a
characteristic orientational `finger print' for the MC anisotropy. However, we
estimate that many hops contribute to conductivity of typical samples, and thus
averaging over critical hop orientations renders the bulk sample isotropic, as
seen experimentally. Anisotropy appears for thin films, when the length of the
hop is comparable to the thickness. The hops are then restricted to align with
the sample plane, leading to different MC behaviors parallel and perpendicular
to it, even after averaging over many hops. We predict the variations of such
anisotropy with both the hop size and the magnetic field strength. An
orientational bias produced by strong electric fields will also lead to MC
anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR
Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance
We study quantum interference effects on the transition strength for strongly
localized electrons hopping on 2D square and 3D cubic lattices in a magnetic
field B. In 2D, we obtain closed-form expressions for the tunneling probability
between two arbitrary sites by exactly summing the corresponding phase factors
of all directed paths connecting them. An analytic expression for the
magnetoconductance, as an explicit function of the magnetic flux, is derived.
In the experimentally important 3D case, we show how the interference patterns
and the small-B behavior of the magnetoconductance vary according to the
orientation of B.Comment: 4 pages, RevTe
Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions
We compute the Coleman Weinberg effective potential for the Higgs field in RS
Gauge-Higgs unification scenarios based on a bulk SO(5) x U(1)_X gauge
symmetry, with gauge and fermion fields propagating in the bulk and a custodial
symmetry protecting the generation of large corrections to the T parameter and
the coupling of the Z to the bottom quark. We demonstrate that electroweak
symmetry breaking may be realized, with proper generation of the top and bottom
quark masses for the same region of bulk mass parameters that lead to good
agreement with precision electroweak data in the presence of a light Higgs. We
compute the Higgs mass and demonstrate that for the range of parameters for
which the Higgs boson has Standard Model-like properties, the Higgs mass is
naturally in a range that varies between values close to the LEP experimental
limit and about 160 GeV. This mass range may be probed at the Tevatron and at
the LHC. We analyze the KK spectrum and briefly discuss the phenomenology of
the light resonances arising in our model.Comment: 31 pages, 9 figures. Corrected typo in boundary condition for gauge
bosons and top mass equation. To appear in PR
Directed paths on hierarchical lattices with random sign weights
We study sums of directed paths on a hierarchical lattice where each bond has
either a positive or negative sign with a probability . Such path sums
have been used to model interference effects by hopping electrons in the
strongly localized regime. The advantage of hierarchical lattices is that they
include path crossings, ignored by mean field approaches, while still
permitting analytical treatment. Here, we perform a scaling analysis of the
controversial ``sign transition'' using Monte Carlo sampling, and conclude that
the transition exists and is second order. Furthermore, we make use of exact
moment recursion relations to find that the moments always determine,
uniquely, the probability distribution $P(J)$. We also derive, exactly, the
moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations
($n\to 0$) to obtain for odd and even moments yield a new signal for
the transition that coincides with Monte Carlo simulations. Analysis of high
moments yield interesting ``solitonic'' structures that propagate as a function
of . Finally, we derive the exact probability distribution for path sums
up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure
Mesoscopic rings with Spin-Orbit interactions
A didactic description of charge and spin equilibrium currents on mesoscopic
rings in the presence of Spin-Orbit interaction is presented. Emphasis is made
on the non trivial construction of the correct Hamiltonian in polar
coordinates, the calculation of eigenvalues and eigenfunctions and the
symmetries of the ground state properties. Spin currents are derived following
an intuitive definition and then a more thorough derivation is built upon the
canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of
the transport problem of spin 1/2 fermions in spin-orbit active media. The
quantization conditions that follow from the constraint of single-valued Pauli
spinors are also discussed. The targeted students are those of a graduate
Condensed Matter Physics course
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