Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models

We propose a simple geometric recipe for constructing phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto the intersecting loop model which is interesting in its own right and is related to several other statistical mechanical models. This mapping is also useful in understanding some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanised phase.Comment: 8 pages, 6 figure

Variational method and duality in the 2D square Potts model

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.Comment: 20 pages, 5 EPS figure

Theory of d-density wave viewed from a vertex model and its implications

The thermal disordering of the $d$-density wave, proposed to be the origin of the pseudogap state of high temperature superconductors, is suggested to be the same as that of the statistical mechanical model known as the 6-vertex model. The low temperature phase consists of a staggered order parameter of circulating currents, while the disordered high temperature phase is a power-law phase with no order. A special feature of this transition is the complete lack of an observable specific heat anomaly at the transition. There is also a transition at a even higher temperature at which the magnitude of the order parameter collapses. These results are due to classical thermal fluctuations and are entirely unrelated to a quantum critical point in the ground state. The quantum mechanical ground state can be explored by incorporating processes that causes transitions between the vertices, allowing us to discuss quantum phase transition in the ground state as well as the effect of quantum criticality at a finite temperature as distinct from the power-law fluctuations in the classical regime. A generalization of the model on a triangular lattice that leads to a 20-vertex model may shed light on the Wigner glass picture of the metal-insulator transition in two-dimensional electron gas. The power-law ordered high temperature phase may be generic to a class of constrained systems and its relation to recent advances in the quantum dimer models is noted.Comment: RevTex4, 10 pages, 11 figure

Reduced disease severity following therapeutic treatment with angiotensin 1-7 in a mouse model of multiple sclerosis

Multiple Sclerosis (MS) is a chronic disease of the central nervous system (CNS) characterized by autoimmune and neurodegenerative pathologies for which there is no cure and no defined etiology. Although several, modestly effective, disease modifying drugs are available to treat MS, there are presently no treatments that offer neuroprotection and prevent clinical progression. Therapies are needed that control immune homeostasis, prevent disease progression, and stimulate regeneration in the CNS. Components of the renin-angiotensin-system (RAS) have recently been identified as chemical mediators in the CNS and in neurological disease. Here we show the beneficial effect of therapeutic treatment with the Mas receptor agonist and metabolite of the protective arm of RAS, angiotensin 1-7 (A(1-7)), in the experimental autoimmune encephalomyelitis (EAE) animal model of MS. Therapeutic treatment with A(1-7) caused a dose-dependent reduction both in clinical disease severity and progression, and was dependent on Mas receptor activation. Further analysis of the most optimal dose of A(1-7) treatment revealed that the reductions in clinical disease course were associated with decreased immune infiltration and demyelination, axonal loss and oxidative stress in the spinal cord. In addition A(1-7) treatment was also associated with increases in circulating alternatively activated monocytes/macrophages.Department of Defense, USC Clinical and Translational Science Institute, National Multiple Sclerosis Society12 month embargo; available online 25 February 2019.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]