A model with simultaneous first and second order phase transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two bond ordered phases, one with local ferromagnetic order and another with local antiferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen. This last result generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue that these phenomena are quite general and should occur for a large class of potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi

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

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

A randomized controlled trial of tea tree oil (5%) body wash versus standard body wash to prevent colonization with methicillin-resistant Staphylococcus aureus (MRSA) in critically ill adults: research protocol

<p>Abstract</p> <p>Background</p> <p>Over the past ten years MRSA has become endemic in hospitals and is associated with increased healthcare costs. Critically ill patients are most at risk, in part because of the number of invasive therapies that they require in the intensive care unit (ICU). Washing with 5% tea tree oil (TTO) has been shown to be effective in removing MRSA on the skin. However, to date, no trials have evaluated the potential of TTO body wash to prevent MRSA colonization or infection. In addition, detecting MRSA by usual culture methods is slow. A faster method using a PCR assay has been developed in the laboratory, but requires evaluation in a large number of patients.</p> <p>Methods/Design</p> <p>This study protocol describes the design of a multicentre, phase II/III prospective open-label randomized controlled clinical trial to evaluate whether a concentration of 5% TTO is effective in preventing MRSA colonization in comparison with a standard body wash (Johnsons Baby Softwash) in the ICU. In addition we will evaluate the cost-effectiveness of TTO body wash and assess the effectiveness of the PCR assay in detecting MRSA in critically ill patients. On admission to intensive care, swabs from the nose and groin will be taken to screen for MRSA as per current practice. Patients will be randomly assigned to be washed with the standard body wash or TTO body wash. On discharge from the unit, swabs will be taken again to identify whether there is a difference in MRSA colonization between the two groups.</p> <p>Discussion</p> <p>If TTO body wash is found to be effective, widespread implementation of such a simple colonization prevention tool has the potential to impact on patient outcomes, healthcare resource use and patient confidence both nationally and internationally.</p> <p>Trial Registration</p> <p>[ISRCTN65190967]</p

Identification of Melatonin-Regulated Genes in the Ovine Pituitary Pars Tuberalis, a Target Site for Seasonal Hormone Control

The pars tuberalis (PT) of the pituitary gland expresses a high density of melatonin (MEL) receptors and is believed to regulate seasonal physiology by decoding changes in nocturnal melatonin secretion. Circadian clock genes are known to be expressed in the PT in response to the decline (Per1) and onset (Cry1) of MEL secretion, but to date little is known of other molecular changes in this key MEL target site. To identify transcriptional pathways that may be involved in the diurnal and photoperiod-transduction mechanism, we performed a whole genome transcriptome analysis using PT RNA isolated from sheep culled at three time points over the 24-h cycle under either long or short photoperiods. Our results reveal 153 transcripts where expression differs between photoperiods at the light-dark transition and 54 transcripts where expression level was more globally altered by photoperiod (all time points combined). Cry1 induction at night was associated with up-regulation of genes coding for NeuroD1 (neurogenic differentiation factor 1), Pbef / Nampt (nicotinamide phosphoribosyltransferase) , Hif1α (hypoxia-inducible factor-1α), and Kcnq5 (K channel) and down-regulation of Rorβ, a key clock gene regulator. Using in situ hybridization, we confirmed day-night differences in expression for Pbef / Nampt, NeuroD1, and Rorβ in the PT. Treatment of sheep with MEL increased PT expression for Cry1, Pbef / Nampt, NeuroD1, and Hif1α, but not Kcnq5. Our data thus reveal a cluster of Cry1-associated genes that are acutely responsive to MEL and novel transcriptional pathways involved in MEL action in the PT

On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\beta$ and random boundary conditions $\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to -). For $\beta$ large enough we show that for any $\epsilon$ there exists $c=c(\beta,\epsilon)$ such that the corresponding mixing time $T_{mix}$ satisfies $\lim_{L\to\infty}P(T_{mix}> \exp({cL^\epsilon})) =0$. In the non-random case $\tau\equiv +$ (or $\tau\equiv -$), this implies that $T_{mix}< \exp({cL^\epsilon})$. The same bound holds when the boundary conditions are all + on three sides and all - on the remaining one. The result, although still very far from the expected Lifshitz behaviour $T_{mix}=O(L^2)$, considerably improves upon the previous known estimates of the form $T_{mix}\le \exp({c L^{1/2 + \epsilon}})$. The techniques are based on induction over length scales, combined with a judicious use of the so-called "censoring inequality" of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.Comment: 39 pages, 8 figures; v2: typos corrected, two references added. To appear on Comm. Math. Phy

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Interfacial adsorption in Potts models on the square lattice

We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., $q = 3$, $4$, and $q = 8$, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point.Comment: 6 pages, 6 eps figures, 1 table, minor corrections, accepted for publication in Eur. Phys. J.

Diurnal rhythmic expression of the rhythm-related genes, rPeriod1, rPeriod2, and rClock , in the rat brain

High densities of the mRNA of three rhythm-related genes, rPeriod1 (rPer1), rPer2 , and rClock , which share high homology in Drosophila and mammals, are found in the rat hypothalamic suprachiasmatic nucleus (SCN). The SCN, however, is not the only brain region that expresses these genes. To understand the possible physiological roles of these rhythm-related genes, we examined expression of these genes in different brain regions at various time points in male Sprague--Dawley rats. Using semi quantitative in situ hybridization with 35 S-riboprobes to evaluate mRNA levels, the diurnal rhythmicity of rPer1, and rPer2 mRNA levels was found in the SCN, arcuate nucleus, and median eminence/pars tuberalis. Expression patterns of mRNA for rPer1 and rPer2 , however, were not similar in these brain regions. The rhythmicity in these brain regions was specific, because it was not observed in the cerebellum or hippocampus. Moreover, diurnal changes in rClock mRNA expression were not detected in any of the brain regions examined. These findings suggest that the different expression patterns observed for rPer1, rPer2 , and rClock mRNAs may be attributed to their different physiological roles in these brain regions, and support previous work indicating that circadian rhythms in the brain are widespread.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43939/1/11373_2004_Article_8176.pd