131 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
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
Low temperature expansion of the gonihedric Ising model
We investigate a model of closed -dimensional soft-self-avoiding
random surfaces on a -dimensional cubic lattice. The energy of a surface
configuration is given by , where is the number of
edges, where two plaquettes meet at a right angle and is the number of
edges, where 4 plaquettes meet. This model can be represented as a
-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic
next-nearest-neighbour- and plaquette-interaction. It corresponds to a special
case of a general class of spin systems introduced by Wegner and Savvidy. Since
there is no term proportional to the surface area, the bare surface tension of
the model vanishes, in contrast to the ordinary Ising model. By a suitable
adaption of Peierls argument, we prove the existence of infinitely many ordered
low temperature phases for the case . A low temperature expansion of the
free energy in 3 dimensions up to order () shows,
that for only the ferromagnetic low temperature phases remain stable. An
analysis of low temperature expansions up to order for the
magnetization, susceptibility and specific heat in 3 dimensions yields critical
exponents, which are in agreement with previous results.Comment: 27 pages, Postscript figures include
Smooth Random Surfaces from Tight Immersions?
We investigate actions for dynamically triangulated random surfaces that
consist of a gaussian or area term plus the {\it modulus} of the gaussian
curvature and compare their behavior with both gaussian plus extrinsic
curvature and ``Steiner'' actions.Comment: 7 page
The QCD string and the generalised wave equation
The equation for QCD string proposed earlier is reviewed. This equation
appears when we examine the gonihedric string model and the corresponding
transfer matrix. Arguing that string equation should have a generalized Dirac
form we found the corresponding infinite-dimensional gamma matrices as a
symmetric solution of the Majorana commutation relations. The generalized gamma
matrices are anticommuting and guarantee unitarity of the theory at all orders
of . In the second quantized form the equation does not have unwanted
ghost states in Fock space. In the absence of Casimir mass terms the spectrum
reminds hydrogen exitations. On every mass level there are different
charged particles with spin running from up to , and the
degeneracy is equal to . This is in contrast with the
exponential degeneracy in superstring theory.Comment: 11 pages LaTeX, uses lamuphys.sty and bibnorm.sty,; Based on talks
given at the 6th Hellenic School and Workshop on Elementary Particle Physics,
Corfu, Greece, September 19-26, 1998 and at the International Workshop
"ISMP", Tbilisi, Georgia, September 12-18, 199
Cooling-rate effects in a model of (ideal?) glass
Using Monte Carlo simulations we study cooling-rate effects in a
three-dimensional Ising model with four-spin interaction. During coarsening,
this model develops growing energy barriers which at low temperature lead to
very slow dynamics. We show that the characteristic zero-temperature length
increases very slowly with the inverse cooling rate, similarly to the behaviour
of ordinary glasses. For computationally accessible cooling rates the model
undergoes an ideal glassy transition, i.e., the glassy transition for very
small cooling rate coincides a thermodynamic singularity. We also study cooling
of this model with a certain fraction of spins fixed. Due to such heterogeneous
crystalization seeds the final state strongly depends on the cooling rate.Only
for sufficiently fast cooling rate does the system end up in a glassy state
while slow cooling inevitably leads to a crystal phase.Comment: 11 pages, 6 figure
Translation invariant extensions of finite volume measures
We investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of ΩΛ for some fixed set Ω, does there exist a measure μ on configurations on all of L, invariant under some specified symme- try group of L, such that μΛ is its marginal on configurations on Λ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L = Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d > 1, the LTI condition is necessary but not sufficient for extendibility. For Zd with d > 1, extendibility is in some sense undecidable
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