101 research outputs found
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.
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
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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