Fluctuations of the free energy in the REM and the p-spin SK models

We consider the random fluctuations of the free energy in the $p$-spin version of the Sherrington-Kirkpatrick model in the high temperature regime. Using the martingale approach of Comets and Neveu as used in the standard SK model combined with truncation techniques inspired by a recent paper by Talagrand on the $p$-spin version, we prove that (for $p$ even) the random corrections to the free energy are on a scale $N^{-(p-2)/4}$ only, and after proper rescaling converge to a standard Gaussian random variable. This is shown to hold for all values of the inverse temperature, \b, smaller than a critical \b_p. We also show that \b_p\to \sqrt{2\ln 2} as $p\uparrow +\infty$. Additionally we study the formal $p\uparrow +\infty$ limit of these models, the random energy model. Here we compute the precise limit theorem for the partition function at {\it all} temperatures. For \b<\sqrt{2\ln2}, fluctuations are found at an {\it exponentially small} scale, with two distinct limit laws above and below a second critical value $\sqrt{\ln 2/2}$: For \b up to that value the rescaled fluctuations are Gaussian, while below that there are non-Gaussian fluctuations driven by the Poisson process of the extreme values of the random energies. For \b larger than the critical $\sqrt{2\ln 2}$, the fluctuations of the logarithm of the partition function are on scale one and are expressed in terms of the Poisson process of extremes. At the critical temperature, the partition function divided by its expectation converges to 1/2.Comment: 40pp, AMSTe

Finite Temperature QCD Sum Rules: a Review

The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.Comment: Minor typos corrected. To be published in the review section of Advances in High Energy Physic

Electromagnetic nucleon form factors from QCD sum rules

The electromagnetic form factors of the nucleon, in the space-like region, are determined from three-point function Finite Energy QCD Sum Rules. The QCD calculation is performed to leading order in perturbation theory in the chiral limit, and to leading order in the non-perturbative power corrections. The results for the Dirac form factor, $F_1(q^2)$, are in very good agreement with data for both the proton and the neutron, in the currently accessible experimental region of momentum transfers. This is not the case, though, for the Pauli form factor $F_2(q^2)$, which has a soft $q^2$-dependence proportional to the quark condensate $$.Comment: Replaced Version. An error has been corrected in the numerical evaluation of the Pauli form factor. This changes the results for F_2(q^2), as well as the conclusion

Chiral symmetry restoration and deconfinement in QCD at finite temperature

The light-quark correlator in the axial-vector channel is used, in conjunction with finite energy QCD sum rules at finite temperature, in order to (a) establish a relation between chiral-symmetry restoration and deconfinement, and (b) determine the temperature behavior of the $a_1(1260)$ width and coupling. Results indicate that deconfinement takes place at a slightly lower temperature than chiral-symmetry restoration, although this difference is not significant given the accuracy of the method. The behaviour of the $a_1(1260)$ parameters is consistent with quark-gluon deconfinement, as the width grows and the coupling decreases with increasing temperature