Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.Comment: 16 page

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

Efficiences économiques comparées des systèmes de production dans différentes situations d'accès à la ressource en eau. Application dans le périmètre irrigué du Gharb, Maroc

International audienceCe travail qui a été mené dans les trois grandes zones d'action de l'ORMVA du Gharb (Côtière, Centrale et Beht) a pour objectifs la comparaison des indices d'efficiences économiques des exploitations agricoles irriguées. La méthode Data Envelopment Analysis (DEA) a été adoptée. Un échantillon de 49 exploitations a servi de base à cette étude. Il englobe des exploitations avec des systèmes de production différents (maraîchers, céréaliers, agrumicoles et sucriers) et des modes d'irrigation différents (localisé, aspersion et gravitaire). L'analyse des données montre que parmi les exploitations les plus efficientes ont trouve en même temps celles qui " souffrent " d'un manque d'eau d'irrigation (zone du Beht) et celles qui ont un accès " illimité " à la ressource (pompages privés au niveau de la zone côtière). La grande majorité (73 %) des exploitations de l'ensemble de l'échantillon sont inefficientes. Ce qui montre que la majorité des agriculteurs ne maîtrise pas la technologie disponible

Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction

We study a one--dimensional Ising spin systems with ferromagnetic, long--range interaction decaying as n^{-2+\a}, \a \in [0,\frac 12], in the presence of external random fields. We assume that the random fields are given by a collection of symmetric, independent, identically distributed real random variables, gaussian or subgaussian with variance $\theta$. We show that for temperature and variance of the randomness small enough, with an overwhelming probability with respect to the random fields, the typical configurations, within volumes centered at the origin whose size grow faster than any power of $\th^{-1}$, % {\bf around the origin} are intervals of $+$ spins followed by intervals of $-$ spins whose typical length is \simeq \th^{-\frac{2}{(1-2\a)}} for 0\le \a<1/2 and $\simeq e^{\frac 1 {\th^{2}}}$ for \a=1/2

Improving estimates of water demand at scheme level using knowledge on farmers' practices

International audienceAccurate estimation of water demand at the irrigation scheme scale is a key requirement for water management, which is made difficult by the large diversity of crops and production systems. The main objective of this study was to estimate irrigation water demand at the farm scale, taking different types of knowledge into account: (i) database study, where water demand is supposed to be the supply (L0); (ii) actual cropping pattern (L1),; (iii) actual irrigation techniques and cropping pattern (L2); and (iv) actual irrigation practices, actual irrigation techniques, and cropping pattern (L3). Farm typology makes easy this estimation as it takes into account various farm characteristics. Firstly, a farm typology was established based on 115 farms surveyed in the irrigation scheme of Borj Toumi Toungar (Tunisia), selected for the study. Secondly, climatic crop water irrigation requirements were estimated using the agro-meteorological water balance model Pilote. Typology results were used to estimate water demand at the scale of family farms taking into account different levels of knowledge Six classes of farming areas were identified based on irrigation subsystems, cropping pattern (fruit tree area, cropping vegetable area and field crop area), intensification crop level and cropped surface. Results showed that supply could not entirely cover the climatic water demand. However, it could nearly meet actual water demand at the farm scale. According to the water demand estimation at different levels, results showed that there were few changes in water demand at farm scale when moving from L1 to L2. At the opposite, actual water demand (L3) represented about half the climatic water demand (L2). Calculations based on farm classes highlighted the importance of actual farm practices. Within the same class, the difference between water demand estimation at different levels of knowledge was remarkable. Network rehabilitation is thus necessary to enable farmers to increase water delivered to crops and limit water stress; the collective network was conceived to deliver a flow of 0.34 l/s/ha in this sector. Given changes in farming and varietal choices, this flow proved insufficient to face the climatic water demand

Phase Transition in the 1d Random Field ising model with long range interaction

We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent identically distributed random variables, subgaussian with mean zero. We show that for temperature and strength of the randomness (variance) small enough with P=1 with respect to the distribution of the random fields there are at least two distinct extremal Gibbs measures