Mott transition in lattice boson models

We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model. The critical line is established to lowest order in the tunneling amplitude.Comment: 20 page

A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model

In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model are convex combinations of the two pure phases. We present here a new approach to this result, with a number of advantages: (i) We obtain an optimal finite-volume, quantitative analogue (implying the classical claim); (ii) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (iii) this new approach might be applicable to systems for which the classical method fails.Comment: A couple of typos corrected. To appear in Probab. Theory Relat. Field

Correlation inequalities for classical and quantum XY models

We review correlation inequalities of truncated functions for the classical and quantum XY models. A consequence is that the critical temperature of the XY model is necessarily smaller than that of the Ising model, in both the classical and quantum cases. We also discuss an explicit lower bound on the critical temperature of the quantum XY model.Comment: 13 pages. Submitted to the volume "Advances in Quantum Mechanics: contemporary trends and open problems" of the INdAM-Springer series, proceedings of the INdAM meeting "Contemporary Trends in the Mathematics of Quantum Mechanics" (4-8 July 2016) organised by G. Dell'Antonio and A. Michelangel

Surface tension in the dilute Ising model. The Wulff construction

We study the surface tension and the phenomenon of phase coexistence for the Ising model on \mathbbm{Z}^d ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random couplings) of surface tension and analyze its large deviations : upper deviations occur at volume order while lower deviations occur at surface order. We study the asymptotics of surface tension at low temperatures and relate the quenched value $\tau^q$ of surface tension to maximal flows (first passage times if $d = 2$). For a broad class of distributions of the couplings we show that the inequality $\tau^a \leqslant \tau^q$ -- where $\tau^a$ is the surface tension under the averaged Gibbs measure -- is strict at low temperatures. We also describe the phenomenon of phase coexistence in the dilute Ising model and discuss some of the consequences of the media randomness. All of our results hold as well for the dilute Potts and random cluster models

Micromechanical modeling-based self-consistent scheme of polymer-layered silicate nanocomposites

Although few investigations recently proposed to describe the overall elastic response of polymer-clay nanocomposites using micromechanical-based models, the applicability of such models for nanocomposites is far from being fully established. In this communication, we present a micromechanical approach for the prediction of the overall moduli of polymer-clay nanocomposites using a self-consistent scheme based on the double-inclusion model. The efficiency of the proposed model to predict the experimental elastic response of various polymer-clay nanocomposites is pointed out

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

MRI study of transient cerebral ischemia in the gerbil: interest of T2 mapping

RATIONALE AND OBJECTIVES: The aim of this study was to evaluate the diagnostic use of MRI and, more precisely, the use of quantitative T2 imaging at 7 T for the early detection of neuronal cerebral alterations after transient ischemia in the gerbil. METHODS: One hundred forty-seven Mongolian gerbils were separated into four groups for which a bicarotid artery occlusion lasted for 4, 6, 8, or 10 minutes, respectively. The animals were scanned before carotid artery occlusion and at 3, 6, 10, 24, and 48 hours and 5 days after the ischemic incident. MR images were acquired on a Bruker Avance DRX300 mini-imaging system. RESULTS: Our results show that T2 mapping is able to localize brain damage induced by transient ischemia and to detect early perturbations in water content (as early as 6 hours after ischemia). CONCLUSIONS: T2 measurements in the striata are correlated with the severity of the ischemic incident, since the changes observed on the T2 images are directly proportional to the duration of occlusion

Recurrent Variational Approach to the Two-Leg Hubbard Ladder

We applied the Recurrent Variational Approach to the two-leg Hubbard ladder. At half-filling, our variational Ansatz was a generalization of the resonating valence bond state. At finite doping, hole pairs were allowed to move in the resonating valence bond background. The results obtained by the Recurrent Variational Approach were compared with results from Density Matrix Renormalization Group.Comment: 10 pages, 14 Postscript figure