Finite Size Effects for the Ising Model Coupled to 2-D Random Surfaces

Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by developing an efficient algorithm for recursively solving the quintic equations so encountered. An analytic method for studying finite size effects is developed based on the behaviour of the free energy near its singular points. The generic form of finite size corrections so obtained are seen to be quite different from the phenomenological parameterisations used in the literature. The method of singularities is also applied to study the magnetic susceptibility. A brief discussion is presented on the implications of these results to the problem of a reliable determination of string susceptibility from numerical simulations.Comment: 18 pages, 3 figure

A scenario for the c>1 barrier in non-critical bosonic strings

The c1 matrix models are analyzed within large N renormalization group, taking into account touching (or branching) interactions. The c<1 modified matrix model with string exponent gamma>0 is naturally associated with an unstable fixed point, separating the Liouville phase (gamma<0) from the branched polymer phase (gamma=1/2). It is argued that at c=1 this multicritical fixed point and the Liouville fixed point coalesce, and that both fixed points disappear for c>1. In this picture, the critical behavior of c>1 matrix models is generically that of branched polymers, but only within a scaling region which is exponentially small when c -> 1. It also explains the behavior of multiple Ising spins coupled to gravity. Large crossover effects occur for c-1 small enough, with a c ~ 1 pseudo-scaling which explains numerical results.Comment: 20 pages, REVTeX3.0 + epsf, 10 figures. 1 reference added. To appear in Nucl. Phys.

Multicanonical simulation of 3D dynamical triangulation model and a new phase structure

We apply the multicanonical technique to the three dimensional dynamical triangulation model, which is known to exhibit a first order phase transition with the Einstein-Hilbert action. We first clarify the first order nature of the phase transition with the Einstein-Hilbert action in several ways including a high precision finite size scaling analysis. We then add a new local term to the action and confirm the conjecture made through the MCRG technique that the line of the first order phase transition extends to the expanded phase diagram, ending at a point. Fractal dimension at the end point is measured to be around three up to the present size.Comment: 20 pages, latex2e(graphic package), 9 figure

Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear in Phys.Rev.

A Korean Family of Hypokalemic Periodic Paralysis with Mutation in a Voltage-gated Calcium Channel (R1239G)

Hypokalemic periodic paralysis (HOPP) is a rare disease characterized by reversible attacks of muscle weakness accompanied by episodic hypokalemia. Recent molecular work has revealed that the majority of familial HOPP is due to mutations in a skeletal muscle voltage-dependent calcium-channel: the dihydropyridine receptor. We report a 13-yr old boy with HOPP from a family in which 6 members are affected in three generations. Genetic examination identified a nucleotide 3705 C to G mutation in exon 30 of the calcium channel gene, CACNA1S. This mutation predicts a codon change from arginine to glycine at the amino acid position #1239 (R1239G). Among the three known mutations of the CACNA1S gene, the R1239G mutation was rarely reported. This boy and the other family members who did not respond to acetazolamide, showed a marked improvement of the paralytic symptoms after spironolactone treatment

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Lattice Investigations of the Running Coupling

A review of investigations of running couplings using lattice techniques is given. This includes i) studies of the running of particular non-perturbatively defined renormalized couplings in pure gauge theories over a range of energies, and ii) how estimates of $\alpha_{\overline{MS}}(m_Z)$ in lattice QCD are presently obtained.Comment: uuencoded postscript fil

Calcium ion currents mediating oocyte maturation events

During maturation, the last phase of oogenesis, the oocyte undergoes several changes which prepare it to be ovulated and fertilized. Immature oocytes are arrested in the first meiotic process prophase, that is morphologically identified by a germinal vesicle. The removal of the first meiotic block marks the initiation of maturation. Although a large number of molecules are involved in complex sequences of events, there is evidence that a calcium increase plays a pivotal role in meiosis re-initiation. It is well established that, during this process, calcium is released from the intracellular stores, whereas less is known on the role of external calcium entering the cell through the plasma membrane ion channels. This review is focused on the functional role of calcium currents during oocyte maturation in all the species, from invertebrates to mammals. The emerging role of specific L-type calcium channels will be discussed