Against Chaos in Temperature in Mean-Field Spin-Glass Models

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.Comment: 20 pages, submitted to J.Phys.

TeV-Scale Black Hole Lifetimes in Extra-Dimensional Lovelock Gravity

We examine the mass loss rates and lifetimes of TeV-scale extra dimensional black holes (BH) in ADD-like models with Lovelock higher-curvature terms present in the action. In particular we focus on the predicted differences between the canonical and microcanonical ensemble statistical mechanics descriptions of the Hawking radiation that results in the decay of these BH. In even numbers of extra dimensions the employment of the microcanonical approach is shown to generally lead to a significant increase in the BH lifetime as in case of the Einstein-Hilbert action. For odd numbers of extra dimensions, stable BH remnants occur when employing either description provided the highest order allowed Lovelock invariant is present. However, in this case, the time dependence of the mass loss rates obtained employing the two approaches will be different. These effects are in principle measurable at future colliders.Comment: 27 pages, 9 figs; Refs. and discussion adde

Aging, memory and rejuvenation: some lessons from simple models

Many recent experiments probed the off equilibrium dynamics of spin glasses and other glassy systems through temperature cycling protocols and observed memory and rejuvenation phenomena. Here we show through numerical simulations, using powerful algorithms, that such features can already be observed to some extent in simple models such as two dimensional ferromagnets. We critically discuss these results and review some aspects of the literature in the light of our findings.Comment: 10 pages, 8 figures. Contribution to the Proceedings of the Summerschool "Ageing and the glass transition", Luxembourg 14-25 Sept. 200

Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

Fragility of the Free-Energy Landscape of a Directed Polymer in Random Media

We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature-chaos. To this end, we combine the replica Bethe ansatz approach outlined in cond-mat/0112384, the mapping to a modified Sinai model and numerically exact calculations by the transfer-matrix method. Our results imply that for all the perturbations under study there is a slow crossover from a weakly perturbed regime where rare events take place to a strongly perturbed regime at larger length scales beyond the so called overlap length where typical events take place leading to chaos, i.e. a complete reshuffling of the free-energy landscape. Within the replica space, the evidence for chaos is found in the factorization of the replicated partition function induced by infinitesimal perturbations. This is the reflex of explicit replica symmetry breaking.Comment: 29 pages, Revtex4, ps figure

Non-linear susceptibilities of spherical models

The static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied. We show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the behaviour of the density of states of the two body interaction matrix in the neighbourhood of the largest eigenvalue. Our results are compared with experimental results and also with those of the droplet theory of spin glasses.Comment: 20 pages, 2 fig

Brane-world black holes and the scale of gravity

A particle in four dimensions should behave like a classical black hole if the horizon radius is larger than the Compton wavelength or, equivalently, if its degeneracy (measured by entropy in units of the Planck scale) is large. For spherically symmetric black holes in 4 + d dimensions, both arguments again lead to a mass threshold MC and degeneracy scale Mdeg of the order of the fundamental scale of gravity MG. In the brane-world, deviations from the Schwarzschild metric induced by bulk effects alter the horizon radius and effective four-dimensional Euclidean action in such a way that MC \simeq Mdeg might be either larger or smaller than MG. This opens up the possibility that black holes exist with a mass smaller than MG and might be produced at the LHC even if M>10 TeV, whereas effects due to bulk graviton exchanges remain undetectable because suppressed by inverse powers of MG. Conversely, even if black holes are not found at the LHC, it is still possible that MC>MG and MG \simeq 1TeV.Comment: 4 pages, no figur

The Particle Physics Reach of High-Energy Neutrino Astronomy

We discuss the prospects for high-energy neutrino astronomy to study particle physics in the energy regime comparable to and beyond that obtainable at the current and planned colliders. We describe the various signatures of high-energy cosmic neutrinos expected in both neutrino telescopes and air shower experiments and discuss these measurements within the context of theoretical models with a quantum gravity or string scale near a TeV, supersymmetry and scenarios with interactions induced by electroweak instantons. We attempt to access the particle physics reach of these experiments.Comment: Mini-review article for New Journal of Physics, "Focus on Neutrinos" issue. 27 pages, 11 figure

Black Holes at the LHC

In these two lectures, we will address the topic of the creation of small black holes during particle collisions in a ground-based accelerator, such as LHC, in the context of a higher-dimensional theory. We will cover the main assumptions, criteria and estimates for their creation, and we will discuss their properties after their formation. The most important observable effect associated with their creation is likely to be the emission of Hawking radiation during their evaporation process. After presenting the mathematical formalism for its study, we will review the current results for the emission of particles both on the brane and in the bulk. We will finish with a discussion of the methodology that will be used to study these spectra, and the observable signatures that will help us identify the black-hole events.Comment: 37 pages, 14 figures, lectures presented in the 4th Aegean Summer School on Black Holes, 17-22 September 2007, Lesvos, Greece, typos corrected, comments and references adde