16467100
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a phantorn crystalline (fixed-connectivity) membrane with free boundary. We verify trie existence of a fiai phase by exarnining lattices of size up to 128~. The Harniltonian of the rnodel is trie sum of a simple spnng pair potential, with no hard-core repulsion, and beuding energy. The only free pararneter is the bending ngidity ~. In-plane elastic constants are non explicitly introduced. We obtain the rernarkable result thon this simple model dynamically generates the elastic constants required to stabilize the fiai phase. We present measurements of the size (Flory) exportent v and the roughness exportent (. We also determine the critical exponents ~ and ~u descnbing the scale dependence of the bending rigidity (~(q) mJ q~~) and trie mduced elastic constants (A(q)mJ ~1(q) ~J q~~ ). Ai bending rigidity ~ = l-1, we find v = 0.95(5) (Hausdorlf dimension dH = 2 Iv = 2,1(1)), ( = 0.64(2 and ~u = 0.50(1). These results are consistent with the scaling relation ( = (2 + ~u)/4. The additional scaling relation ~ = 2(1- () irnplies ~ = 0.72(4). A direct measurernent of ~ from the power-law decay of the normal-normal correlation functiou yields ~ m 0.6 on the 128~ lattice.
122263335
Multiple Ising models coupled to 2-d gravity: a CSD analysis
Abstract We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.
119499105
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In particular we give the phase diagram and critical exponents for phantom membranes and discuss the generalization to self-avoiding membranes.
12041139
The flat phase of fixed-connectivity membranes
Abstract The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system [1]. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.
8220387
Phantom Tubules
We provide the first numerical evidence for the existence of the tubule phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes. Incorporating anisotropy into the bending rigidity of a simple model of a phantom tethered membrane with the topology of a disk and free boundary conditions we show that the model indeed has two phase transitions corresponding to the flat-to-tubule and tubule-to-crumpled transitions. For the tubule phase we measure the Flory exponent νF , describing the growth of the tubule radius with the extent of the tubule, and the roughness exponent ζ, which measures the r.m.s. height fluctuations in the extended direction. We find νF = 0.305(14) and ζ = 0.895(60) which are in reasonable agreement with the theoretical predictions of RT, νF = 1/4 and ζ = 1. PACS numbers: 64.60.Fr, 05.40.+j, 82.65.Dp Typeset using REVTEX
9011435
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
Abstract We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
121504553
On the masses of the glueballs in pure SU(2) lattice gauge theory
Abstract Using a Monte Carlo method to measure the correlation functions of different quantities, the mass spectrum of the glue-ball is investigated for an SU(2) gauge model in an 8 4 lattice.
119852951
On the link between strong and weak coupling expansions for the SU(2) lattice gauge theory
The intermediate region between the strong and weak coupling expansions of SU(2) lattice gauge theory is analyzed by inverting the strong coupling series of the average plaquette energy Ep(J). 
 
Taking into account the weak coupling behaviour too, we get Pade approximants for J(Ep) valid in the whole physical region. The zeros of pJ/pEp are mapped into singularities of Ep(J); they occur for complex values of J and give rise to a peak in the specific heat in fair agreement with the Monte Carlo simulation data. The variable Ep is further used to analyze the strong coupling expansions for the roughening indicator, the string tension and the mass gap.
121490138
On the effects of an uncertainty on the evolution law in dynamical systems
We show that a small perturbation of the evolution law of chaotic dynamical systems is practically equivalent to the finite precision on the knowledge of the initial condition. In spite of the short predictability time tp on a single trajectory we found that the statistical properties are not sensitive to small changes in the evolution law or initial probability distribution. This feature holds also for correlation functions at a delay larger than tp. We discuss the roundoff effects on integrable systems.
121714112
A Monte Carlo simulation with an “improved” action for the O(3) non-linear sigma model
Abstract We present the results of a Monte Carlo simulation for a lattice action improved a la Symanzik. The results seem to give a faster approach of the lattice physics to its continuum limit.
123085141
Intermittency and Multifractality in Magnetic Dynamos
We study the convection of magnetic fields in the presence of Lagrangian chaos, i.e. when nearby fluid elements diverge exponentially in time. We show that the magnetic field is of a multifractal nature as a consequence of the spatial fluctuations in the exponential growth of the field. We provide numerical and theoretical evidence that the magnetic fields can concentrate in small domains of a fluid with weak Lagrangian chaos. Moreover, these properties are relevant also for the study of the case of small but nonzero magnetic diffusivity.