8,162 research outputs found
The Complexity of the Spherical -spin spin glass model, revisited
Some questions concerning the calculation of the number of ``physical''
(metastable) states or complexity of the spherical -spin spin glass model
are reviewed and examined further. Particular attention is focused on the
general calculation procedure which is discussed step-by-step.Comment: 13 pages, 3 figure
Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation
A careful critical analysis of the complexity, at the annealed level, of the
Sherrington-Kirkpatrick model has been performed. The complexity functional is
proved to be always invariant under the Becchi-Rouet-Stora-Tyutin
supersymmetry, disregarding the formulation used to define it. We consider two
different saddle points of such functional, one satisfying the supersymmetry
[A. Cavagna {\it et al.}, J. Phys. A {\bf 36} (2003) 1175] and the other one
breaking it [A.J. Bray and M.A. Moore, J. Phys. C {\bf 13} (1980) L469]. We
review the previews studies on the subject, linking different perspectives and
pointing out some inadequacies and even inconsistencies in both solutions.Comment: 20 pages, 4 figure
Large Extra Dimensions at Linear Colliders
In this talk, I first present the motivation for theories wherein extra
spacetime dimensions can be compactified to have large magnitudes. In
particular, I discuss the Arkani-Hamed, Dimopoulos, Dvali (ADD) scenario. I
present the constraints that have been derived on these models from current
experiments and the expectations from future colliders. I concentrate
particularly on the possibilities of probing these extra dimensions at future
linear colliders.Comment: Talk given at the Third International Workshop on Electron-Electron
Interactions at TeV Energies (e- e- 99), Santa Cruz, California, 10-12 Dec
1999. 7 pages, LaTeX, style files attache
Complexity in Mean-Field Spin-Glass Models: Ising -spin
The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising
-spin is investigated in the temperature regime where the equilibrium phase
is one step Replica Symmetry
Breaking. Two solutions of the resulting saddle point equations are found.
One is supersymmetric (SUSY) and includes the equilibrium value of the free
energy while the other is non-SUSY. The two solutions cross exactly at a value
of the free energy where the replicon eigenvalue is zero; at low free energy
the complexity is described by the SUSY solution while at high free energy it
is described by the non-SUSY solution. In particular the non-SUSY solution
describes the total number of solutions, like in the
Sherrington-Kirkpatrick (SK) model. The relevant TAP solutions corresponding
to the non-SUSY solution share the same feature of the corresponding solutions
in the SK model, in particular their Hessian has a vanishing isolated
eigenvalue. The TAP solutions corresponding to the SUSY solution, instead, are
well separated minima.Comment: 13 pages, 9 figure
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