5,286 research outputs found
Complex and Non-Complex Phase Structures in Models of Spin Glasses and Information Processing
The gauge theory of spin glasses and statistical-mechanical formulation of
error-correcting codes are reviewed with an emphasis on their similarities. For
the gauge theory, we explain the functional identities on dynamical
autocorrelation functions and on the distribution functions of order
parameters. These functional identities restrict the possibilities of slow
dynamics and complex structure of the phase space. An inequality for
error-correcting codes is shown to be interpreted to indicate non-monotonicity
of spin orientation as a function of the temperature in spin glasses.Comment: 13 pages; Proceedings of the International Symposium on Slow Dynamics
in Nature, Seoul, Korea, November 2001; to be published in Physica
Torsion points of abelian varieties with values in infinite extensions over a p-adic field
Let be an abelian variety over a -adic field and an algebraic
infinite extension over . We consider the finiteness of the torsion part of
the group of rational points under some assumptions. In 1975, Hideo Imai
proved that such a group is finite if has good reduction and is the
cyclotomic -extension of . In this talk, first we show a
generalization of Imai's result in the case where has ordinary good
reduction. Next we give some finiteness results when is an elliptic curve
and is the field generated by the -power torsion of an elliptic curve
Four-Dimensional Planck Scale is Not Universal in Fifth Dimension in Randall-Sundrum Scenario
It has recently been proposed that the hierarchy problem can be solved by
considering the warped fifth dimension compactified on . Many
studies in the context have assumed a particular choice for an integration
constant that appears when one solves the five-dimensional
Einstein equation. Since is not determined by the boundary
condition of the five-dimensional theory, may be regarded as a
gauge degree of freedom in a sense. To this time, all indications are that the
four-dimensional Planck mass depends on . In this paper, we
carefully investigate the properties of the geometry in the Randall-Sundrum
model, and consider in which location the four-dimensional Planck mass is
measured. As a result, we find a -independent relation between the
four-dimensional Planck mass and five- dimensional fundamental
mass scale , and remarkably enough, we can take to TeV region when we
consider models with the Standard Model confined on a distant brane. We also
confirm that the physical masses on the distant brane do not depend on
by considering a bulk scalar field as an illustrative example. The
resulting mass scale of the Kaluza-Klein modes is on the order of .Comment: Latex, 12 page
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