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A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins., Reviews results in arXiv:1106.0325 and arXiv:1106.4664 in light of more recent simulations and fracton literature. Published in special issue of Entropy dedicated to the memory of Professor Ian Campbell

An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (Phys. Rev. Lett. 28 (1972) 507), who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (Phys. Rev. B 81 (2010) 184303). We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions., v5 - The title is changed to better reflect the contents and the exposition is streamlined. Version accepted for publication

The overall incidence of gestational diabetes mellitus (GDM) is increasing worldwide. Preventing pathological hyperglycaemia during pregnancy could have several benefits: a reduction in the immediate adverse outcomes during pregnancy, a reduced risk of long-term sequelae and a decrease in the economic burden to healthcare systems. In this Review we examine the evidence supporting lifestyle modification strategies in women with and without risk factors for GDM, and the efficacy of dietary supplementation and pharmacological approaches to prevent this disease. A high degree of heterogeneity exists between trials so a generalised recommendation is problematic. In population studies of dietary or combined lifestyle measures, risk of developing GDM is not improved and those involving a physical activity intervention have yielded conflicting results. In pregnant women with obesity, dietary modification might reduce fetal macrosomia but in these patients, low compliance and no significant reduction in the incidence of GDM has been observed in trials investigating physical activity. Supplementation with probiotics or myoinositol have reduced the incidence of GDM but confirmatory studies are still needed. In randomized controlled trials, metformin does not prevent GDM in certain at-risk groups. Given the considerable potential for reducing disease burden, further research is needed to identify strategies that can be easily and effectively implemented on a population level.

The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of β ∞ = 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension σ = 0.12037(18), using the statistics of suppressed configurations. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

We investigate whether the dynamical lattice supersymmetry discussed for various Hamiltonians, including one-dimensional quantum spin chains, by (Fendley et al 2003 J. Phys. A 36, 12399424; Yang and Fendley 2004 J. Phys. A 37, 893748; Hagendorf and Fendley 2012 J. Stat. Phys. 146, 112255) and (Hagendorf et al 2013 J. Stat. Phys. 150, 60957; Hagendorf and Liénardy 2017 J. Phys. A 50, 185202; Hagendorf and Liénardy 2018 J. Stat. Mech. 033106) might also exist for the Markov matrices of any one-dimensional exclusion processes, which have the additional constraint of zero column sums by comparison with the spin chains. We find that the DiSSEP (Dissipative Symmetric Simple Exclusion Process), introduced by Crampe et al in (Crampe et al 2016 Phys. Rev. E 94, 032102; Vanicat [arXiv:1708.02440]), provides one such example for suitably chosen parameters. The DiSSEP Markov matrix admits the supersymmetry in these cases because it is conjugate to Ising (λ 2 = 1) and Δ = −1/2 XXZ (λ 2 = −3) spin chain Hamiltonians which also possess the supersymmetry. The consequences for the spectrum of the DiSSEP Markov matrix are discussed. We also note that the length-changing supersymmetry relation for the DiSSEP Markov matrix M L and the supercharge Q L† for L sites, M L Q L † = Q L † M L − 1 , is reminiscent of a ‘transfer matrix’ symmetry that has been observed in other exclusion processes and discuss the similarity.

Background: The Advanced Bolus Calculator for Diabetes (ABC4D) is an insulin bolus dose decision support system based on case-based reasoning (CBR). The system is implemented in a smartphone application to provide personalized and adaptive insulin bolus advice for people with type 1 diabetes. We aimed to assess proof of concept, safety, and feasibility of ABC4D in a free-living environment over 6 weeks. Methods: Prospective nonrandomized single-arm pilot study. Participants used the ABC4D smartphone application for 6 weeks in their home environment, attending the clinical research facility weekly for data upload, revision, and adaptation of the CBR case base. The primary outcome was postprandial hypoglycemia. Results: Ten adults with type 1 diabetes, on multiple daily injections of insulin, mean (standard deviation) age 47 (17), diabetes duration 25 (16), and HbA1c 68 (16) mmol/mol (8.4 (1.5) %) participated. A total of 182 and 150 meals, in week 1 and week 6, respectively, were included in the analysis of postprandial outcomes. The median (interquartile range) number of postprandial hypoglycemia episodes within 6-h after the meal was 4.5 (2.0–8.2) in week 1 versus 2.0 (0.5–6.5) in week 6 (P = 0.1). No episodes of severe hypoglycemia occurred during the study. Conclusion: The ABC4D is safe for use as a decision support tool for insulin bolus dosing in self-management of type 1 diabetes. A trend suggesting a reduction in postprandial hypoglycemia was observed in the final week compared with week 1.

The normal pancreatic f-cell membrane depolarizes in response to increasing concentrations of glucose in a bursting pattern. At 7 m M (126 mg/dl) until a continuous train of bursting is seen at >25 m M (450 mg/dl). A bio-inspired silicon device has been developed using analogue electronics to implement membrane depolarization of the β cell. The device is ultralow powered, miniaturized (5 × 5 mm), and produces a bursting output identical to that characterized in electrophysiological studies. Objective: The goal of this study was to demonstrate the ability of silicon implementation of β-cell electrophysiology to respond to a simulated glucose input and to drive an infusion pump in vitro. Method: The silicon device response to a current source was recorded at varying simulated glucose concentrations. Subsequently, the bursting response to a changing analyte concentration measured by an amperometric enzyme electrode was converted to a voltage, driving a syringe pump loaded with a 50-ml syringe containing water. Results: Bursting responses are comparable to those recorded in electrophysiology. Silicon β-cell implementation bursts with a pulse width proportional to concentration and is able to drive an infusion pump. Conclusion: This is the first in vitro demonstration of closed loop insulin delivery utilizing miniaturized silicon implementation of β-cell physiology in analogue electronics.

We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour ∝ 1/L 3 to 1/L 2. The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.

In this paper we conduct a careful multicanonical simulation of the isotropic $3d$ plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low- and high-temperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility $\chi_m$ seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. $\chi_m$ is therefore not a suitable order parameter for the model., Comment: The discussion of the treatment of errors is expanded, the description of the variable transformation in the anisotropic case is clarified, various minor typos are fixed and some references have been added

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 figure

The Gonihedric Ising model is a particular case of the class of models defined by Savvidy and Wegner intended as discrete versions of string theories on cubic lattices. In this paper we perform a high statistics analysis of the phase transition exhibited by the 3d Gonihedric Ising model with $k=0$ in the light of a set of recently stated scaling laws applicable to first order phase transitions with fixed boundary conditions. Even though qualitative evidence was presented in a previous paper to support the existence of a first order phase transition at $k=0$, only now are we capable of pinpointing the transition inverse temperature at $\beta_c = 0.54757(63)$ and of checking the scaling of standard observables., Comment: 14 pages, 5 tables, 2 figures, uses elsart.cls package

Background Different time-concentration profiles of plasma insulin following insulin modification of a frequently sampled intravenous glucose-tolerance-test (FSIVGTT) were observed in a study investigating maternal metabolism and fetal macrosomia. We aimed to investigate whether these differences were related to the volume of distribution of insulin, insulin clearance, or both. Design Forty-four women were studied between 33 and 35 weeks’ gestation using an insulin-modified FSIVGTT. Specific insulin was assayed with an enzyme-linked immunosorbent assay. Insulin sensitivity was calculated using the minimal model and the homeostasis model assessment (HOMA). The volume of distribution and clearance of insulin were calculated from measurements between 2 and 155 min after insulin modification using a one-compartment model. Results In accordance with the method for deriving the volume of distribution, there was a significant negative correlation between the increment in insulin concentration and the volume of distribution (rho = −0·92, P

A well-known feature of first-order phase transitions is that fixed boundary conditions can strongly influence finite-size corrections, modifying the leading corrections for an L3 lattice in 3d from order 1/L3 under periodic boundary conditions to 1/L. A rather similar effect, albeit of completely different origin, occurs when the system possesses an exponential low- temperature phase degeneracy of the form 23L which causes for periodic boundary conditions a leading correction of order 1/L2 in 3d. We discuss a 3d plaquette Hamiltonian ("gonihedric") Ising model, which displays such a degeneracy and manifests the modified scaling behaviour. We also investigate an apparent discrepancy between the fixed and periodic boundary condition latent heats for the model when extrapolating to the thermodynamic limit.

The purely plaquette 3d Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, "fuki-nuke" order still exists and we confirm this with multicanonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analysing our measurements., Comment: arXiv admin note: text overlap with arXiv:1412.4426

Discretized formulations of 2-form Abelian and non-Abelian gauge fields on $d$-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards [J. High Energy Phys. 09 (2014) 034]. In this paper we recall that the Hamiltonian of a ${\mathbb{Z}}_{2}$ variant of such theories is one of the family of generalized Ising models originally considered by Wegner. For such ``${\mathbb{Z}}_{2}$ lattice Gerbe theories'' general arguments can be used to show that a phase transition for Wilson surfaces will occur for $dg3$ between volume and area scaling behavior. In $3d$ the model is equivalent under duality to an infinite coupling model and no transition is seen, whereas in $4d$ the model is dual to the $4d$ Ising model and displays a continuous transition. In $5d$ the ${\mathbb{Z}}_{2}$ lattice Gerbe theory is self-dual in the presence of an external field and in $6d$ it is self-dual in zero external field.

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x L lattice in 3D) is transmuted to 1/L^2 scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical simulations of this model to generate high-precision data which provides strong confirmation of the non-standard finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the non-standard scaling., Comment: Minor change of title (canonical ->standard) to match the version accepted for publication, some further explanation on numerical subtleties added, wider applicability of effect discussed, typos (hopefully) fixed, references added

We report on single-cluster Monte Carlo simulations of the Ising, 4-state Potts and 10-state Potts models on quenched ensembles of planar, tri-valent random graphs. We confirm that the first-order phase transition of the 10-state Potts model on regular 2D lattices is softened by the quenched connectivity disorder represented by the random graphs and that the exponents of the Ising and 4-state Potts models are altered from their regular lattice counterparts. The behaviour of spin models on such graphs is thus more analogous to models with quenched bond disorder than to Poisonnian random lattices, where regular lattice critical behaviour persists. Using a wide variety of estimators we measure the critical exponents for all three models, and compare the exponents with predictions derived from taking a quenched limit in the KPZ formula for the Ising and 4-state Potts models. Earlier simulations suggested that the measured values for the 10-state Potts model were very close to the predicted quenched exponents of the {\it four}-state Potts models. The analysis here, which employs a much greater range of estimators and also benefits from greatly improved statistics, still supports these numerical values., Comment: 14 pages (latex) + 6 latex tables + 5 figures

Under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system. Here we discuss a series of Monte Carlo studies of a special type of such disordered systems, namely spin models dened on quenched, random lattices exhibiting geometrical disorder in the connectivity of the lattice sites. In two dimensions we present results for the q-state Potts model on random tri-valent ( 3 ) planar graphs, which appear quite naturally in the dynamically triangulated random surface (DTRS) approach to quantum gravity, as well as on Poissonian random lattices of Voronoi=Delaunay type. Both cases, q64 and >4, are discussed which, in the pure model without disorder, give rise to second- and rst-order phase transitions, respectively. In three dimensions results for the Ising model on Poissonian random lattices are briey described. We conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder, and a discussion of the distinguishing dierences. c 2000 Elsevier Science B.V. All rights reserved.

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles., Latex, 10 pages plus 6 ps/eps figures

Recently we have found identical behaviour for various spin models on `thin' random graphs - Feynman diagrams - and the corresponding Bethe lattices. In this paper we observe that the ratios of the saddle-point equations in the random graph approach are identical to the fixed point(s) of the recursion relations which are used to solve the models on the Bethe lattice. The loops in the random graphs thus have no influence on the thermodynamic limit for such ferromagnetic spin models. We consider the correspondence explicitly for Ising and q state Potts models and also note that multispin interaction models on cacti admit a similar correspondence with a randomized version of the cacti graphs which contain loops.

It is known that fixed boundary conditions modify the leading finite-size corrections for an L 3 lattice in 3 d at a first-order phase transition from 1/ L 3 to 1/ L . We note that an exponential low-temperature phase degeneracy of the form 2 3L will lead to a different leading correction of order 1/ L 2 . A 3 d gonihedric Ising model with a four-spin interaction, plaquette Hamiltonian displays such a degeneracy and we confirm the modified scaling behaviour using high-precision multicanonical simulations. We remark that other models such as the Ising antiferromagnet on the FCC lattice, in which the number of “true” low-temperature phases is not macroscopically large but which possess an exponentially degenerate number of low lying states may display an ef- fective version of the modified scaling law for the range of lattice sizes accessible in simulations.

We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit are locally tree-like, in distinction to the ``fat'' random graphs that appear in the planar Feynman diagram limit, more familiar from discretized models of two dimensional gravity. The interest of the thin graphs is that they give mean field theory behaviour for spin models living on them without infinite range interactions or the boundary problems of genuine tree-like structures such as the Bethe lattice. q-state Potts models display a first order transition in the mean field for q>2, so the thin graph Potts models provide a useful test case for exploring discontinuous transitions in mean field theories in which many quantities can be calculated explicitly in the saddle point approximation., 10 pages, latex, + 6 postscript figures

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, StLouis

We investigate a three-dimensional Ising action which corresponds to a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the couplings are tuned in such a way that the action depends only on the angles of the discrete surface, i.e. on the way the surface is embedded in . Hence the name gonihedric by which they are known. We show that the model displays a rather clear first-order phase transition in the limit where self-avoidance is neglected and the action becomes a plaquette one. This transition persists for small values of the self avoidance coupling, but it turns to second-order when this latter parameter is further increased. These results exclude the use of this type of action as models of gonihedric random surfaces, at least in the limit where self avoidance is neglected.

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs., (2) Minor typos corrected, references updated

We study the dynamical out-of-equilibrium behavior of a $J = \pm 1$ Ising spin glass on quenched $\phi^{3}$ graphs. We show that magnetization and energy decay with a power law behavior, with exponents that are linear in $\frac{T}{T_{c}}$. Quenched $\phi^{3}$ graphs turn out to be a very effective way to study numerically mean field spin glasses.

We perform simulations of an absolute value version of the Villain model on φ3 and φ4 Feynman diagrams, “thin” 3-regular and 4-regular random graphs. The φ4 results are in excellent quantitative agreement with the exact calculations by Dorey and Kurzepa for an annealed ensemble of thin graphs, in spite of simulating only a single graph of each size. We also derive exact results for an annealed ensemble of φ3 graphs and again find excellent agreement with the numerical data for single φ3 graphs. The simulations confirm the picture of a mean field vortex transition which is suggested by the analytical results. Further simulations on φ5 and φ6 graphs and of the standard XY model on φ3 graphs confi the universality of these results. The calculations of Dorey and Kurzepa were based on reinterpreting the large orders behaviour of the anharmonic oscillator in a statistical mechanical context so we also discuss briefly the interpretation of singularities in the large orders behaviour in other models as phase transitions.

The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q=2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second- to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent Blume-Emery-Griffiths model. Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q=2 case, r_c(z)=[4 z / 3(z-1)] [(z-1)/(z-2)]^z invisible states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z=3, the 3-regular, random-graph result is recovered, while the infinite z limit delivers the Bragg-Williams, mean-field result.

Microneedle array devices provide the opportunity to overcome the barrier characteristics of the outermost skin layer, the stratum corneum. This novel technology can be used as a therapeutic tool for transdermal drug delivery, including insulin, or as a diagnostic tool providing access to dermal biofluids, with subsequent analysis of its contents. Over the last decade, the use of microneedle array technology has been the focus of extensive research in the field of transdermal drug delivery. More recently, the diagnostic applications of microneedle technology have been developed. This review summarizes the existing evidence for the use of microneedle array technology as biosensors for continuous monitoring of the glucose content of interstitial fluid, focusing also on mechanics of insertion, microchannel characteristics, and safety profile.

A 3D Ising model with a purely plaquette, 4-spin interaction displays a planar flip symmetry intermediate between a global and a gauge symmetry and as a consequence has a highly degenerate low temperature phase and no standard magnetic order parameter. This plaquette Hamiltonian is a particular case of a family of 3D gonihedric Ising models defined by Savvidy and Wegner. An anisotropic variant of the purely plaquette gonihedric model, originally discussed as the ?Fuki-Nuke? model by Suzuki, is non-trivially equivalent to a stack of 2D Ising models, each of which can magnetize independently at the phase transition point. Consideration of this anisotropic model suggests that a suitable order parameter in the isotropic case may also be constructed using a form of planar magnetization, in which nearest neighbour correlators ??i?j? summed over planes replace a sum over spin values ??i?. We conduct Monte-Carlo simulations to investigate this and related candidate order parameters in a toy model of gonihedric ground states, the Fuki-Nuke model and the isotropic plaquette gonihedric model itself.

The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For antiferromagnetic couplings the replica trick gives some evidence for a spin glass phase. In this paper we investigate both the ferromagnetic and antiferromagnetic models with the aid of simulations. We confirm the Bethe lattice values of the critical points for the ferromagnetic model on $\phi^3$ and $\phi^4$ graphs and examine the putative spin glass phase in the antiferromagnetic model by looking at the overlap between replicas in a quenched ensemble of graphs. We also compare the Ising results with those for higher state Potts models and Ising models on ``fat'' graphs, such as those used in 2D gravity simulations., Comment: LaTeX 13 pages + 9 postscript figures, COLO-HEP-340, LPTHE-Orsay-94-62

We simulate the Ising model on a set of fixed random $\phi^3$ 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 $\phi^3$ graphs, flat lattices and a single fixed $\phi^3$ graph., Comment: 8 pages

It has been suggested that the peak in the specific heat observed numerically for random surface actions with extrinsic curvature on dynamical lattices might be the result of a low mass bound state in an asymptotically free theory, rather than the signal for a real phase transition. The O(3) model on a fixed lattice displays just such behavior, but in general peaks appear to be weakened when the models concerned are put on dynamical lattices (i.e., coupled to two-dimensional quantum gravity). We therefore perform simulations of the O(3) model on dynamical ${\ensuremath{\varphi}}^{3}$ graphs to see if there is still a peak in the specific heat and compare the results with those on fixed lattices.

We investigate the dual of the kappa=0 Gonihedric Ising model on a 3D cubic lattice, which may be written as an anisotropically coupled Ashkin-Teller model. The original kappa=0 Gonihedric model has a purely plaquette interaction, displays a first order transition and possesses a highly degenerate ground state. We find that the dual model admits a similar large ground state degeneracy as a result of the anisotropic couplings and investigate the coupled mean field equations for the model on a single cube. We also carry out Monte Carlo simulations which confirm a first order phase transition in the model and suggest that the ground state degeneracy persists throughout the low temperature phase. Some exploratory cooling simulations also hint at non-trivial dynamical behaviour., 17 pages, 12 figures

We perform simulations of a discrete gaussian solid on solid (DGSOS) model on dynamical $\phi^3$ 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.

We investigate the crossover between weak and strong self-avoidance in a simulation of random surfaces with extrinsic curvature. We consider both dynamically triangulated and rigid surfaces with the two possible discretizations of the extrinsic curvature term., Comment: 5 pages

We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$., 9 pages

We note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process (PASEP) lends itself to interpretation as the transfer matrix for weighted Motzkin lattice paths. A continued fraction ("J-Fraction") representation of the lattice path generating function is particularly well suited to discussing the PASEP, for which the paths have height dependent weights. We show that this not only allows a succinct derivation of the normalisation and correlation lengths of the PASEP, but also reveals how finite-dimensional representations of the PASEP algebra, valid only along special lines in the phase diagram, relate to the general solution that requires an infinite-dimensional representation.

We introduce an explicit local self-avoidance in both fixed and dynamically triangulated random surfaces with a gaussian (Polyakov) plus extrinsic curvature action in the hope that this might approximate a superstring model. We look at the effect this has on the crumpling transitions exhibited by the surfaces embedded in three dimensions and contrast the results with those obtained in simulations of self-avoiding tethered and fluid membranes in the context of solid state physics.

We examine further the critical behaviour of dynamically triangulated random surfaces (DTRS) with extrinsic curvature at their second-order crumpling transition. We show that the string tension in these models may be scaling near the transition in such a way that the physical string tension is finite, unlike models containing only a Polyakov term, suggesting that one can use DTRS as a discretization of subcritical string theory. We explore the universality properties of DTRS, showing that an apparently irrelevant term can affect the phase transition. We also find that the observed phase transition persists when the surfaces are embedded in higher dimensions, contradicting the naive expectations of a saddle point expansion.

The papers in this special section are devoted to the topic of ways in which biomedical technologies and informatics are being used in the management of diabetes. It is estimated that 371 million people worldwide have diabetes and the number is increasing at an alarming rate. In addition to short-term symptoms, there are long-term macro and microvascular complications including cardiovascular disease, especially heart attacks and strokes, kidney failure, diabetic foot disease leading to gangrene and amputation, and blindness.

We review the status of lattice computer calculations in Quantum Chromo-dynamics (QCD) and mention a new field of computational high-energy physics—that of Strings or random surfaces. After outlining Monte Carlo Field Theory we explain in detail both QCD and Strings—describing how these theories are discretized on a lattice, what one can calculate, and how much computer time is required. We include a summary of the concurrent QCD machines which have been, and are being, built. We speculate on the prospects for such work, including a prediction for when QCD will besolved!

Earlier simulations of dynamically triangulated random surfaces with a pure Gaussian (Polyakov) action have suggested that the incorporation of a term which is equivalent to the square of the scalar curvature, R2, in the continuum can affect the properties of the surfaces, despite the fact that such a term appears to be irrelevant on dimensional grounds. However, simulations by the current authors and Catterall of dynamically triangulated random surfaces with extrinsic curvature produced essentially identical results despite differing coefficients for the R2 term. In this short note we show that small (positive or negative) values of this coefficient have little effect but that large values to produce measurable effects. This explains the concordance of our previous results with Catterall’s and also provides evidence for non-universal behavior in the random surface model.

We present the results of a numerical simulation of dynamically triangulated random surfaces of fixed topology with extrinsic curvature. We use two different discretizations of the extrinsic curvature and observe the differing nature of the crumpling transitions and smooth phases. The effect of the extrinsic curvature on both the extrinsic and intrinsic geometry of the model is examined in three and four dimensions. We also discuss the similarities between our simulation and those of surfaces of fixed triangulation and consider the connection between models with extrinsic curvature and superstrings.

We briefly outline string theory, explain how it is formulated discretely on a computer in terms of dynamically triangulated random surfaces, and describe a computer program that simulates such surfaces with extrinsic curvature embedded in arbitrary dimension.

We review a class of 3D lattice spin models in which planar Peierls boundaries between + and - spins can be created at zero energy cost. These so-called Gonihedric Ising models have (in general) specially tuned nearest neighbour, next-to-nearest neighbour and plaquette interactions, which endow the models with some novel properties both in and out of equilibrium.

Four dimensional simplicial gravity has been studied by means of Monte Carlo simulations for some time, the main outcome of the studies being that the model undergoes a discontinuous phase transition between an elongated and a crumpled phase when one changes the curvature (Newton) coupling. In the crumpled phase there are singular vertices growing extensively with the volume of the system whereas the elongated phase resembles a branched-polymer. We have postulated that this behaviour is a manifestation of the constrained-mean-field scenario as realised in the Branched Polymer or Balls-in-Boxes model. These models share all the features of 4D simplicial gravity except that they exhibit a continuous phase transition. We note here that this defect can be remedied by a suitable choice of ensemble., 3 pages, LaTeX, 2 figures, uses espcrc2.sty, talk given at LATTICE97

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature., 4 pages