Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model

In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale N^{-1/2}, for N large. The method we employ is based on the idea, we recently developed, of introducing quadratic coupling between two replicas. The proof makes use of the cavity equations and of concentration of measure inequalities for the free energy.Comment: 18 page

The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas, let us say a, and the added s+1 is either independent of the former ones, or it is identical to one of the overlaps q(a,b), with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su.se/stefano/ms/ghigu.p

Does postoperative radiation therapy represent a contraindication to expander-implant based immediate breast reconstruction? An update 2012-2014

Post-mastectomy radiotherapy (PMRT) is well known in the plastic surgery community for having a negative impact on expander-implant based immediate breast reconstruction (IBBR), although recently some technical improvements allow better results. Very recent papers would suggest that there is no difference in postoperative complications in patients receiving post-mastectomy radiotherapy using modern techniques. However, study results are often biased by small groups of patients and by heterogeneity of radiotherapy timing, different surgical techniques and measured outcomes

Local Spin Glass Order in 1D

We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.Comment: 17 page

An Extended Variational Principle for the SK Spin-Glass Model

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound, as well as the actual value, are obtained through an optimization procedure for which ultrametic/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex

Optimization of graphene-based materials outperforming host epoxy matrices

The degree of graphite exfoliation and edge-carboxylated layers can be controlled and balanced to design lightweight materials characterized by both low electrical percolation thresholds (EPT) and improved mechanical properties. So far, this challenging task has been undoubtedly very hard to achieve. The results presented in this paper highlight the effect of exfoliation degree and the role of edge-carboxylated graphite layers to give self-assembled structures embedded in the polymeric matrix. Graphene layers inside the matrix may serve as building blocks of complex systems that could outperform the host matrix. Improvements in electrical percolation and mechanical performance have been obtained by a synergic effect due to finely balancing the degree of exfoliation and the chemistry of graphene edges which favors the interfacial interaction between polymer and carbon layers. In particular, for epoxy-based resins including two partially exfoliated graphite samples, differing essentially in the content of carboxylated groups, the percolation threshold reduces from 3 wt% down to 0.3 wt%, as the carboxylated group content increases up to 10 wt%. Edge-carboxylated nanosheets also increase the nanofiller/epoxy matrix interaction, determining a relevant reinforcement in the elastic modulus

Mean field dilute ferromagnet I. High temperature and zero temperature behavior

We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero magnetization from the phase with symmetry breaking. We also compute exactly the entropy at temperature zero, which is strictly positive. The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation, and suggests possible behaviors at generic low temperatures. Lastly, we provide a complete solution for the annealed model. Our results hold both for the Poisson and the Bernoulli versions of the model.Comment: 38 page