6,989 research outputs found

### $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators

We study the statistical mechanics of a $D$-dimensional array of Josephson
junctions in presence of a magnetic field. In the high temperature region the
thermodynamical properties can be computed in the limit $D \to \infty$, where
the problem is simplified; this limit is taken in the framework of the mean
field approximation. Close to the transition point the system behaves very
similar to a particular form of spin glasses, i.e. to gauge glasses. We have
noticed that in this limit the evaluation of the coefficients of the high
temperature expansion may be mapped onto the computation of some matrix
elements for the $q$-deformed harmonic oscillator

### Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses

We compute numerically small window overlaps in the three dimensional Edwards
Anderson spin glass. We show that they behave in the way implied by the Replica
Symmetry Breaking Ansatz, that they do not qualitatively differ from the full
volume overlap and do not tend to a trivial function when increasing the
lattice volume. On the contrary we show they are affected by small finite
volume effects, and are interesting tools for the study of the features of the
spin glass phase.Comment: 9 pages plus 5 figure

### The ideal glass transition of Hard Spheres

We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.Comment: 13 pages, 8 figure

### A variational approach to Ising spin glasses in finite dimensions

We introduce a hierarchical class of approximations of the random Ising spin
glass in $d$ dimensions. The attention is focused on finite clusters of spins
where the action of the rest of the system is properly taken into account. At
the lower level (cluster of a single spin) our approximation coincides with the
SK model while at the highest level it coincides with the true $d$-dimensional
system. The method is variational and it uses the replica approach to spin
glasses and the Parisi ansatz for the order parameter. As a result we have
rigorous bounds for the quenched free energy which become more and more precise
when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J.
Phys. A: Math. Ge

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