40 research outputs found
Frustrating and Diluting Dynamical Lattice Ising Spins
We investigate what happens to the third order ferromagnetic phase transition
displayed by the Ising model on various dynamical planar lattices (ie coupled
to 2D quantum gravity) when we introduce annealed bond disorder in the form of
either antiferromagnetic couplings or null couplings. We also look at the
effect of such disordering for the Ising model on general and
Feynman diagrams.Comment: 7pages, LaTex , LPTHE-ORSAY-94-5
Is There Quantum Gravity in Two Dimensions?
A hybrid model which allows to interpolate between the (original) Regge
approach and dynamical triangulations is introduced. The gained flexibility in
the measure is exploited to study dynamical triangulation in a fixed geometry.
Our numerical results support KPZ exponents. A critical assessment concerning
the apparent lack of gravitational effects in two dimensions follows.Comment: 20 pages including 4 figures, uuencoded Z-compressed .tar file
created by uufile
Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations
We write down matrix models for Ising spins with zero external field on the
vertices of dynamical triangulated random surfaces (DTRS) and dynamically
quadrangulated random surfaces (DQRS) and compare these with the standard
matrix model approach which places the spins on the dual and
graphs. We show that the critical temperatures calculated in the DTRS and DQRS
models agree with those deduced from duality arguments in the standard
approach. Using the DQRS model we observe that the Ising antiferromagnet still
undergoes a phase transition to a Neel (checkerboard) ordered ground state
which is absent because of frustration in the other cases.Comment: 5 pages, late
The critical behaviour of Ising spins on 2D Regge lattices
We performed a high statistics simulation of Ising spins coupled to 2D
quantum gravity on toroidal geometries. The tori were triangulated using the
Regge calculus approach and contained up to vertices. We used a
constant area ensemble with an added interaction term, employing the
measure. We find clear evidence that the critical exponents of the Ising
phase transition are consistent with the static critical exponents and do not
depend on the coupling strength of the interaction term. We definitively
can exclude for this type of model a behaviour as predicted by Boulatov and
Kazakov [Phys. Lett. {\bf B186}, 379 (1987)] for Ising spins coupled to
dynamically triangulated surfaces.Comment: 15 pages with 3 figures in form of an uudecoded compressed
tar-ps-file. FUB-HEP 06/9
Dynamically Triangulated Ising Spins in Flat Space
A model describing Ising spins with short range interactions moving randomly
in a plane is considered. In the presence of a hard core repulsion, which
prevents the Ising spins from overlapping, the model is analogous to a
dynamically triangulated Ising model with spins constrained to move on a flat
surface. It is found that as a function of coupling strength and hard core
repulsion the model exhibits multicritical behavior, with first and second
order transition lines terminating at a tricritical point. The thermal and
magnetic exponents computed at the tricritical point are consistent with the
exact two-matrix model solution of the random Ising model, introduced
previously to describe the effects of fluctuating geometries.Comment: (10 pages + 4 figures), CERN-Th-7577/9
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
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
Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it
multiple} state Potts models on dynamical phi-cubed graphs of
spherical topology in order to investigate the region of two-dimensional
quantum gravity. Contrary to naive expectation we find no obvious signs of
pathological behaviour for . We discuss the results in the light of
suggestions that have been made for a modified DDK ansatz for .Comment: 9 page
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
Segregation trends of the metal alloys Mo-Re and Mo-Pt on HfO2: A first-principles study
Using first-principles calculations, we compared the segregation trends at the surface of metal alloys with those at an interface with HfO2. The choice of this oxide was motivated by its significance as a potential replacement for SiO2 in advanced transistors. We considered Mo-Re and Mo-Pt alloys as typical examples of disordered and ordered alloys, respectively. The segregation to the surface/interface was analyzed in terms of metal and oxygen adsorption energies. It is shown that chemical bonding at the metal/oxide interface strongly influences segregation both in Mo-Re and Mo-Pt alloys. In particular, bonding with oxygen atoms at the oxide/Mo-Re alloy interface depletes the Re content of the interfacial layer. In the case of Mo-Pt on HfO2 an oxygen-rich interface promotes the formation of one monolayer (but not two monolayers) of Mo separating PtMox from HfO2, while a stoichiometric interface favors an abrupt PtMox/HfO2 interface. This study also shows that the presence of Mo in the alloy stabilizes Pt which can potentially decrease the tendency of Pt to diffuse into the oxide matrix. The individual constituents of these intermetallic compounds exhibit high vacuum work functions, and therefore these alloys are also likely to have sufficiently high work functions to be considered as promising candidates for p-type gate electrodes in future generations of transistors. (c) 2006 American Institute of Physics.100