1,406 research outputs found
Euclidean Field Theory
A coincise review about Euclidean (Quantum) Field Theory is presented. It
deals with the general structural properties, the connections with Quantum
Field Theory, the exploitation in Constructive Quantum Field Theory, and the
physical interpretation.Comment: 19 page
Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
By using a simple interpolation argument, in previous work we have proven the
existence of the thermodynamic limit, for mean field disordered models,
including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here
we extend this argument in order to compare the limiting free energy with the
expression given by the Parisi Ansatz, and including full spontaneous replica
symmetry breaking. Our main result is that the quenched average of the free
energy is bounded from below by the value given in the Parisi Ansatz uniformly
in the size of the system. Moreover, the difference between the two expressions
is given in the form of a sum rule, extending our previous work on the
comparison between the true free energy and its replica symmetric
Sherrington-Kirkpatrick approximation. We give also a variational bound for the
infinite volume limit of the ground state energy per site.Comment: 16 page
The high temperature region of the Viana-Bray diluted spin glass model
In this paper, we study the high temperature or low connectivity phase of the
Viana-Bray model. This is a diluted version of the well known
Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric
region, we obtain a complete control of the system, proving annealing for the
infinite volume free energy, and a central limit theorem for the suitably
rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy
fluctuations, on the scale 1/N, converge in the infinite volume limit to a
non-Gaussian random variable, whose variance diverges at the boundary of the
replica-symmetric region. The connection with the fully connected
Sherrington-Kirkpatrick model is discussed.Comment: 24 page
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