298 research outputs found
A Lower Estimate for the Modified Steiner Functional
We prove inequality (1) for the modified Steiner functional A(M), which
extends the notion of the integral of mean curvature for convex surfaces.We
also establish an exression for A(M) in terms of an integral over all
hyperplanes intersecting the polyhedralral surface M.Comment: 6 pages, Late
Phase Transition in Lattice Surface Systems with Gonihedric Action
We prove the existence of an ordered low temperature phase in a model of
soft-self-avoiding closed random surfaces on a cubic lattice by a suitable
extension of Peierls contour method. The statistical weight of each surface
configuration depends only on the mean extrinsic curvature and on an
interaction term arising when two surfaces touch each other along some contour.
The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version
of the gonihedric string, which is an action for triangulated random surfaces.Comment: 17 pages, Postscript figures include
On subdivision invariant actions for random surfaces
We consider a subdivision invariant action for dynamically triangulated
random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys.
Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical
partition function is infinite for all values of the coupling constants. We
conjecture that adding the area action to the action of Ambartzumian et. al.
leads to a well-behaved theory.Comment: 7 pages, Latex, RH-08-92 and YITP/U-92-3
Geometrical String and Spin Systems
We formulate a new geometrical string on the euclidean lattice. It is
possible to find such spin systems with local interaction which reproduce the
same surface dynamics.In the three-dimensional case this spin system is a usual
Ising ferromagnet with additional diagonal antiferromagnetic interaction and
with specially adjusted coupling constants. In the four-dimensional case the
spin system coincides with the gauge Ising system with an additional
double-plaquette interaction and also with specially tuned coupling constants.
We extend this construction to random walks and random hypersurfaces (membrane
and p-branes) of high dimensionality. We compare these spin systems with the
eight-vertex model and BNNNI models.Comment: 10 pages, Latex,Crete-TH-5-July-199
Gonihedric Ising Actions
We discuss a generalized Ising action containing nearest neighbour, next to
nearest neighbour and plaquette terms that has been suggested as a potential
string worldsheet discretization on cubic lattices by Savvidy and Wegner. This
displays both first and second order transitions depending on the value of a
``self-intersection'' coupling as well as possessing a novel semi-global
symmetry.Comment: Latex + 2 postscript figures. Poster session contribution to
"Lattice96" conference, Washington University, StLoui
Curvature representation of the gonihedric action
We analyse the curvature representation of the gonihedric action for
the cases when the dependence on the dihedral angle is arbitrary.Comment: 10 pages, LaTeX, 3 embedded figures with psfig, submitted to
Phys.Lett.
The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation
Given a potential of pair interaction and a value of activity, one can
consider the Gibbs distribution in a finite domain . It is well known that for small values of activity there exist
the infinite volume () limiting Gibbs distribution
and the infinite volume correlation functions. In this paper we consider the
converse problem - we show that given and , where
is a constant and is a function on , which are
sufficiently small, there exist a pair potential and a value of activity, for
which is the density and is the pair correlation function
Steiner Variations on Random Surfaces
Ambartzumian et.al. suggested that the modified Steiner action functional had
desirable properties for a random surface action. However, Durhuus and Jonsson
pointed out that such an action led to an ill-defined grand-canonical partition
function and suggested that the addition of an area term might improve matters.
In this paper we investigate this and other related actions numerically for
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page
The Phase Diagram of the Gonihedric 3d Ising Model via CVM
We use the cluster variation method (CVM) to investigate the phase structure
of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The
geometrical spin cluster boundaries in these systems serve as models for the
string worldsheets of the gonihedric string embedded in . The models
are interesting from the statistical mechanical point of view because they have
a vanishing bare surface tension. As a result the action depends only on the
angles of the discrete surface and not on the area, which is the antithesis of
the standard 3d Ising model.
The results obtained with the CVM are in good agreement with Monte Carlo
simulations for the critical temperatures and the order of the transition as
the self-avoidance coupling is varied. The value of the magnetization
critical exponent , calculated with the cluster
variation--Pad\`e approximant method, is also close to the simulation results.Comment: 8 pages text (LaTex) + 3 eps figures bundled together with uufile
Self-Avoiding Gonihedric Srting and Spin Systems
We classify different theories of self-intersecting random surfaces assigning
special weights to intersections. When self-intersection coupling constant
tends to zero, then the surface can freely inetrsect and it is
completely self-avoiding when tends to infinity. Equivalent spin
systems for this general case were constructed. In two-dimension the system
with is in complete disorder as it is in the case of 2D gauge
Ising system.Comment: Preprint CRETE-TH-21, October 1993,8 pages,Late
- …