575888
Fluid random surfaces with extrinsic curvature. II
Abstract We present the results of an extension of our previous work on large-scale simulations of dynamically triangulated toroidal random surfaces embedded in R 3 with extrinsic curvature. We find that the extrinsic-curvature specific heat peak ceases to grow on lattices with more than 576 nodes and that the location of the peak λ c also stabilizes. The evidence for a true crumpling transition is still weak. If we assume it exists we can say that the finite-size scaling exponent α / ηd is very close to zero or negative. On the other hand our new data does rule out the observed peak as being a finite-size artifact of the persistence length becoming comparable to the extent of the lattice.
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.
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.
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.
14633114
The phase diagram of crystalline surfaces
We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to 128 2 nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.
122714395
Passive-Scalar Fluctuations in Intermittent Turbulence
We discuss how the spatial intermittency of energy dissipation in 3D fully developed turbulence affects the small-scale statistics of passive scalars. We relate the passive-scalar behaviour to the diffusion properties of particle pairs in turbulent fluids. We thus find the intermittency correction to the -5/3 Obukhov-Corrsin law for the power spectrum of a passive scalar at wavenumber k where molecular diffusion and viscosity play a negligible role (inertial convective subrange). This correction is positive at difference with the negative correction to the -5/3 Kolmogorov law for the energy spectrum. We finally show that the structure functions of passive scalars have scaling exponents linear in the moment order, even in the framework of multifractal models.
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.
120014368
A new proposal for the determination of the renormalization group trajectories by the Monte Carlo renormalization group method
Abstract We present a new method for calculating block renormalized couplings by Monte Carlo renormalization group. This method has several advantages with respect to the existing ones and can be applied for any value of the coupling constants. A preliminary numerical study of the 2-dimensional O(3) non linear σ-model is also presented.
120236230
An evaluation of parity-violating effects in low-energy pion-nucleon scattering
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.