240,003 research outputs found
Self-consistency and Symmetry in d-dimensions
Bethe approximation is shown to violate Bravais lattices translational
invariance. A new scheme is then presented which goes over the one-site Weiss
model yet preserving initial lattice symmetry. A mapping to a one-dimensional
finite closed chain in an external field is obtained. Lattice topology
determines the chain size. Using recent results in percolation, lattice
connectivity between chains is argued to be where is the
coordination number and is the space dimension. A new self-consistent
mean-field equation of state is derived. Critical temperatures are thus
calculated for a large variety of lattices and dimensions. Results are within a
few percent of exact estimates. Moreover onset of phase transitions is found to
occur in the range . For the Ising hypercube it yields the Golden
number limit .Comment: 16 pages, latex, Phys. Rev. B (in press
Baryon-Pion Couplings from Large-N QCD
We derive a set of consistency conditions for the pion-baryon coupling
constants in the large-N limit of QCD. The consistency conditions have a unique
solution which are precisely the values for the pion-baryon coupling constants
in the Skyrme model. We also prove that non-relativistic spin-flavor
symmetry (where is the number of light flavors) is a symmetry of the
baryon-pion couplings in the large-N limit of QCD. The symmetry breaking
corrections to the pion-baryon couplings vanish to first order in .
Consistency conditions for other couplings, such as the magnetic moments are
also derived.Comment: (12 pages, 2 figs, uses harvmac and uufiles), UCSD/PTH 93-1
Symmetries and itineracy in nonlinear systems with many degrees of freedom
Tsuda examines the potential contribution of nonlinear dynamical systems, with many degrees of freedom, to understanding brain function. We offer suggestions concerning symmetry and transients to strengthen the physiological motivation and theoretical consistency of this novel research direction: Symmetry plays a fundamental role, theoretically and in relation to real brains. We also highlight a distinction between chaotic "transience" and "itineracy"
Soft Theorems For Shift-Symmetric Cosmologies
We derive soft theorems for single-clock cosmologies that enjoy a shift
symmetry. These so-called consistency conditions arise from a combination of a
large diffeomorphism and the internal shift-symmetry and fix the squeezed limit
of all correlators with a soft scalar mode. As an application, we show that our
results reproduce the squeezed bispectrum for Ultra-slow-roll inflation, a
particular shift-symmetric, non-attractor model which is known to violate
Maldacena's consistency relation. Similar results have been previously obtained
by Mooij and Palma using background-wave methods. Our results shed new light on
the infrared structure of single-clock cosmological spacetimes.Comment: 4 pages, v2: citation added, v3: citations added and edited in
accordance with published versio
Heterotic T-Duality and the Renormalization Group
We consider target space duality transformations for heterotic sigma models
and strings away from renormalization group fixed points. By imposing certain
consistency requirements between the T-duality symmetry and renormalization
group flows, the one loop gauge beta function is uniquely determined, without
any diagram calculations. Classical T-duality symmetry is a valid quantum
symmetry of the heterotic sigma model, severely constraining its
renormalization flows at this one loop order. The issue of heterotic anomalies
and their cancelation is addressed from this duality constraining viewpoint.Comment: 17 pages, Late
The full replica symmetry breaking in the Ising spin glass on random regular graph
In this paper, we extend the full replica symmetry breaking scheme to the
Ising spin glass on a random regular graph. We propose a new martingale
approach, that overcomes the limits of the Parisi-M\'ezard cavity method,
providing a well-defined formulation of the full replica symmetry breaking
problem in random regular graphs. Finally, we define the order parameters of
the system and get a set of self-consistency equations for the order parameters
and the free energy. We face up the problem only from a technical point of
view: the physical meaning of this approach and the quantitative evaluation of
the solution of the self-consistency equations will be discussed in next works.Comment: 23 page
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