arXiv subjects

Mark Bowick

Publications and source records attributed to Mark Bowick.

26 records · Page 2Linked to original sources

arXiv1996

Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71 degrees) or with that of a regular octahedron (109 degrees). We study this model in the presence of a negative bending rigidity K, which favours the folding process. We use both a cluster variation method (CVM) approximation and a transfer matrix approach. The system is shown to undergo two separate geometrical transitions with increasing |K|: a first discontinuous transition separates a phase where the triangular lattice is preferentially wrapped around octahedra from a phase where it is preferentially wrapped around tetrahedra. A second continuous transition separates this latter phase from a phase of complete folding of the lattice on top of a single triangle.

cond-mat.stat-mech↗

arXiv1996

Discrete Folding

Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a face-centered-cubic lattice are treated. The 3d-folding problem corresponds to a 96-vertex model and exhibits a first-order folding transition from a crumpled phase to a completely flat phase as the bending rigidity increases.

cond-mat.stat-mech↗

arXiv1995

Two Ising Models Coupled to 2-Dimensional Gravity

To investigate the properties of $c=1$ matter coupled to $2$d{--}gravity we have performed large-scale simulations of two copies of the Ising Model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents using finite-size scaling. We show explicitly how logarithmic corrections are needed for a proper comparison with theoretical exponents. We also exhibit correlations, mediated by gravity, between the energy and magnetic properties of the two Ising species. The prospects for extending this work beyond $c=1$ are addressed.

hep-th↗

arXiv1993

Fluid Random Surfaces with Extrinsic Curvature: II

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 $\lam_c$ 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 $\frac α {νd}$ 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.

hep-th↗

arXiv1992

The Phase Structure of Strings with Extrinsic Curvature

We examine a model of non-self-avoiding, fluctuating surfaces as a candidate continuum string theory of surfaces in three dimensions. This model describes Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze, using Monte Carlo simulations, the dramatic crossover behaviour of several observables which characterize the geometry of these surfaces. We then critically discuss whether our observations are indicative of a phase transition.

hep-th↗

arXiv1992

Strings with Extrinsic Curvature: An Analysis of the Crossover Regime

We present the results of a set of Monte Carlo simulations of Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze several observables in the crossover regime and discuss whether or not our observations are indicative of the presence of a phase transition.

hep-lat↗

arXiv1992

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

I report on the observation of the production of strings (disclination lines and loops) via the Kibble mechanism of domain (bubble) formation in the isotropic to nematic phase transition of a sample of uniaxial nematic liquid crystal. The probablity of string formation per bubble is measured to be $0.33 \pm 0.01$. This is in good agreement with the theoretical value $1/ π$ expected in two dimensions for the order parameter space $S^2/{\bf Z}_2$ of a simple uniaxial nematic liquid crystal. ( NB: The only change is a correction of the preprint number for proper referencing and the title page.)

hep-th↗

arXiv1992

The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature

We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling analysis to characterize as much as possible the regime of crossover from crumpled to smooth surfaces.

hep-lat↗