Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Fluctuation Bounds For Interface Free Energies in Spin Glasses

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.Comment: 19 pages, 0 figure

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

Intravenous Artesunate for Severe Malaria

OBJECTIVE: To review the pharmacodynamics and pharmacotherapeutic use of intravenous artesunate for the treatment of severe malaria. DATA SOURCES: Literature was retrieved through PubMed (1999 March 2010), MEDLINE (1996 March 2010), and the Centers for Disease Control and Prevention (CDC), using the search terms artemisinin, artesunate, malaria, and severe malaria. In addition, reference citations from publications identified were reviewed. STUDY SELECTION AND DATA EXTRACTION: All articles in English that were identified from the data sources were reviewed. Focus was placed on post-marketing trials examining the safety and efficacy of artesunate in comparison with other regimens. DATA SYNTHESIS: The treatment of severe malaria requires prompt, safe, and effective intravenous antimalarials. Many oral and intravenous agents are available worldwide for the treatment of malaria; however, quinidine has been the only option for parenteral therapy in the US. Furthermore, this product\u27s lack of availability as well as its adverse safety profile have created a treatment option gap. Recently, intravenous artesunate was approved by the Food and Drug Administration (FDA) for investigational drug use and distribution by the CDC. Three major studies regarding the use of intravenous artesunate are reviewed, in addition to the World Health Organization\u27s malaria treatment guidelines. While there are no published head-to-head trials of intravenous artesunate versus intravenous quinidine for severe malaria, several international studies comparing intravenous quinine and artesunate concluded that artesunate has the highest treatment success, with lower incidence of adverse events. In addition, other literature is reviewed regarding counterfeit and other issues associated with artesunate. CONCLUSIONS: Artesunate, a new antimalarial currently available through the CDC, appears to be highly effective, better tolerated than quinidine, and not hampered by accessibility issues. If it were to be FDA approved and commercially available, it would be the preferred agent for the treatment of severe malaria in the US

Stochastic Stability: a Review and Some Perspectives

A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.Comment: 12 pages, typos corrected, references added. To appear in Journal of Statistical Physics, Special Issue for the 100th Statistical Mechanics Meetin

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha)$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha|J)$ is supported on a single ground state pair.Comment: 20 pages, 3 figure

Short-range spin glasses and Random Overlap Structures

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.Comment: 27 page

A unified stability property in spin glasses

Gibbs' measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current understanding of these models. In this paper we show that one can combine these two properties very naturally into one unified stability property