266 research outputs found
Softening Transitions with Quenched 2D Gravity
We perform extensive Monte Carlo simulations of the 10-state Potts model on
quenched two-dimensional gravity graphs to study the effect of
quenched connectivity disorder on the phase transition, which is strongly first
order on regular lattices. The numerical data provides strong evidence that,
due to the quenched randomness, the discontinuous first-order phase transition
of the pure model is softened to a continuous transition.Comment: 3 pages, LaTeX + 1 postscript figure. Talk presented at
LATTICE96(other models). See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
Square Gravity
We simulate the Ising model on dynamical quadrangulations using a
generalization of the flip move for triangulations with two aims: firstly, as a
confirmation of the universality of the KPZ/DDK exponents of the Ising phase
transition, worthwhile in view of some recent surprises with other sorts of
dynamical lattices; secondly, to investigate the transition of the Ising
antiferromagnet on a dynamical loosely packed (bipartite) lattice. In the
latter case we show that it is still possible to define a staggered
magnetization and observe the antiferromagnetic analogue of the transition.Comment: LaTeX file and 7 postscript figures bundled together with uufile
Spin Models on Thin Graphs
We discuss the utility of analytical and numerical investigation of spin
models, in particular spin glasses, on ordinary ``thin'' random graphs (in
effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two
dimensional gravity. We highlight the similarity with Bethe lattice
calculations and the advantages of the thin graph approach both analytically
and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy
compressed ps file replaced with uuencoded LaTex original + ps figure
Two distinct types of neuronal asymmetries are controlled by the Caenorhabditis elegans zinc finger transcription factor die-1
Left/right asymmetric features of animals are either randomly distributed on either the left or right side within a population ("antisymmetries") or found stereotypically on one particular side of an animal ("directional asymmetries"). Both types of asymmetries can be found in nervous systems, but whether the regulatory programs that establish these asymmetries share any mechanistic features is not known. We describe here an unprecedented molecular link between these two types of asymmetries in Caenorhabditis elegans. The zinc finger transcription factor die-1 is expressed in a directionally asymmetric manner in the gustatory neuron pair ASE left (ASEL) and ASE right (ASER), while it is expressed in an antisymmetric manner in the olfactory neuron pair AWC left (AWCL) and AWC right (AWCR). Asymmetric die-1 expression is controlled in a fundamentally distinct manner in these two neuron pairs. Importantly, asymmetric die-1 expression controls the directionally asymmetric expression of gustatory receptor proteins in the ASE neurons and the antisymmetric expression of olfactory receptor proteins in the AWC neurons. These asymmetries serve to increase the ability of the animal to discriminate distinct chemosensory inputs
Quenching 2D Quantum Gravity
We simulate the Ising model on a set of fixed random graphs, which
corresponds to a {\it quenched} coupling to 2D gravity rather than the annealed
coupling that is usually considered. We investigate the critical exponents in
such a quenched ensemble and compare them with measurements on dynamical
graphs, flat lattices and a single fixed graph.Comment: 8 page
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
Damaging 2D Quantum Gravity
We investigate numerically the behaviour of damage spreading in a Kauffman
cellular automaton with quenched rules on a dynamical graph, which is
equivalent to coupling the model to discretized 2D gravity. The model is
interesting from the cellular automaton point of view as it lies midway between
a fully quenched automaton with fixed rules and fixed connectivity and a
(soluble) fully annealed automaton with varying rules and varying connectivity.
In addition, we simulate the automaton on a fixed graph coming from a
2D gravity simulation as a means of exploring the graph geometry.Comment: 6 pages, COLO-HEP-332;LPTHE-Orsay-93-5
Scaling in Steiner Random Surfaces
It has been suggested that the modified Steiner action functional has
desirable properties for a random surface action. In this paper we investigate
the scaling of the string tension and massgap in a variant of this action on
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.Comment: 7 pages, COLO-HEP-32
Spin Glasses on Thin Graphs
In a recent paper we found strong evidence from simulations that the
Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed
amean-field spin glass transition. The intrinsic interest of considering such
random graphs is that they give mean field results without long range
interactions or the drawbacks, arising from boundary problems, of the Bethe
lattice. In this paper we reprise the saddle point calculations for the Ising
and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We
use standard results from bifurcation theory that enable us to treat an
arbitrary number of replicas and any quenched bond distribution. We note the
agreement between the ferromagnetic and spin glass transition temperatures thus
calculated and those derived by analogy with the Bethe lattice, or in previous
replica calculations. We then investigate numerically spin glasses with a plus
or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models,
paying particular attention to the independence of the spin glass transition
from the fraction of positive and negative bonds in the Ising case and the
qualitative form of the overlap distribution in all the models. The parallels
with infinite range spin glass models in both the analytical calculations and
simulations are pointed out.Comment: 13 pages of LaTex and 11 postscript figures bundled together with
uufiles. Discussion of first order transitions for three or more replicas
included and similarity to Ising replica magnet pointed out. Some additional
reference
Dgsos on DTRS
We perform simulations of a discrete gaussian solid on solid (DGSOS) model on
dynamical graphs, which is equivalent to coupling the model to 2d
quantum gravity, using the cluster algorithms recently developed by Evertz
et.al.for use on fixed lattices. We find evidence from the growth of the
width-squared in the rough phase of KT-like behaviour, which is consistent with
theoretical expectations. We also investigate the cluster statistics, dynamical
critical exponent and lattice properties, and compare these with the dual XY
model.Comment: 9 pages, COLO-HEP-32
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