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 $\phi^3$ and $\phi^4$ Feynman diagrams.Comment: 7pages, LaTex , LPTHE-ORSAY-94-5

Softening Transitions with Quenched 2D Gravity

We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional $\Phi^3$ 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

Information Geometry and Phase Transitions

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur

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

Thin Fisher zeros

Various authors have suggested that the loci of partition function zeros can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeros for Ising and Potts models on non-planar ('thin') regular random graphs using this approach, and note that the locus of Fisher zeros on a Bethe lattice is identical to the corresponding random graph. Since the number of states q appears as a parameter in the Potts solution the limiting locus of chromatic zeros is also accessible

Percutaneous endoscopic gastrostomy: Indications, technique and complications at Groote Schuur Hospital

Percutaneous endoscopic gastrostomy (PEG) is a relatively new technique in South Africa. It is useful in the management of patients with neurological and oropharyngeal disorders in whom long-term feeding is necessary. The PEGs inserted in patients at Groote Schuur Hospital between June 1986 and March 1990 as part of an on-going study to evaluate this procedure are reported

Vertex Models on Feynman Diagrams

The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in complex matrix models, which describes vertex models of different sorts living on random graphs. From the graph theoretic perspective one is using matrix model and field theory inspired methods to count various classes of directed graphs. We also make some remarks on vertex models on planar random graphs (the N --> infinity limit) where the resulting matrix models are not generally soluble using currently known methods. Nonetheless, some particular cases may be mapped onto known models and hence solved.Comment: 10 Pages text (LaTeX), 4 eps figure

Fat and Thin Fisher Zeroes

We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high- and low-temperature branches of the expression for the free energy. Similar methods work for the mean-field model on generic, ``thin'' graphs. Series expansions are very easy to obtain for such random graph Ising models.Comment: 3 pages, LaTeX, Lattice2001(surfaces

Freezing in random graph ferromagnets

Using T=0 Monte Carlo and simulated annealing simulation, we study the energy relaxation of ferromagnetic Ising and Potts models on random graphs. In addition to the expected exponential decay to a zero energy ground state, a range of connectivities for which there is power law relaxation and freezing to a metastable state is found. For some connectivities this freezing persists even using simulated annealing to find the ground state. The freezing is caused by dynamic frustration in the graphs, and is a feature of the local search-nature of the Monte Carlo dynamics used. The implications of the freezing on agent-based complex systems models are briefly considered.Comment: Published version: 1 reference deleted, 1 word added. 4 pages, 5 figure

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 ${\bf Z}^3$. 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 $\kappa$ is varied. The value of the magnetization critical exponent $\beta = 0.062 \pm 0.003$, 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