Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

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 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, 0.12037(18), using the statistics of suppressed configurations

Macroscopic Degeneracy and order in the 3d plaquette Ising model

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:1412.442

Exact solutions to plaquette Ising models with free and periodic boundaries

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.Comment: v5 - The title is changed to better reflect the contents and the exposition is streamlined. Version accepted for publicatio

Z2\mathbb{Z}_2 Lattice Gerbe Theory

$2$-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. In this note 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 $d>3$ between volume and area scaling behaviour. 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.Comment: v2: references added, abstract tweaked, (at least some of the) timeline clarifie

The Wrong Kind of Gravity

The KPZ formula shows that coupling central charge less than one spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on the central charge. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins. Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the ``wrong'' central charge. We might then expect to see the critical exponents appropriate to the central charge used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the Ising, tricritical Ising and 3-state Potts models.Comment: 8 pages, no figure

On Random Allocation Models in the Thermodynamic Limit

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover new relationships between the thermodynamic potentials and fill some lacunae in previous results on the singularities of these potentials at the critical point and behaviour in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulae step by step throughout. Additionally, we comment on a quasi-probabilistic normalisation of configuration weights which has been considered in some recent studie

Finite-size scaling and latent heat at the gonihedric first-order phase transition

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

Softening of First-Order Phase Transition on Quenched Random Gravity Graphs

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 coordination number randomness on the nature of 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, representing presumably a new universality class. This result is in striking contrast to a recent Monte Carlo study of the 8-state Potts model on two-dimensional Poissonian random lattices of Voronoi/Delaunay type, where the phase transition clearly stayed of first order, but is in qualitative agreement with results for quenched bond randomness on regular lattices. A precedent for such softening with connectivity disorder is known: in the 10-state Potts model on annealed Phi3 gravity graphs a continuous transition is also observed.Comment: Latex + 5 postscript figures, 10 pages of text, figures appende

Effect of rosiglitazone on progression of atherosclerosis: insights using 3D carotid cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>There is recent evidence suggesting that rosiglitazone increases death from cardiovascular causes. We investigated the direct effect of this drug on atheroma using 3D carotid cardiovascular magnetic resonance.</p> <p>Results</p> <p>A randomized, placebo-controlled, double-blind study was performed to evaluate the effect of rosiglitazone treatment on carotid atherosclerosis in subjects with type 2 diabetes and coexisting vascular disease or hypertension. The primary endpoint of the study was the change from baseline to 52 weeks of carotid arterial wall volume, reflecting plaque burden, as measured by carotid cardiovascular magnetic resonance. Rosiglitazone or placebo was allocated to 28 and 29 patients respectively. Patients were managed to have equivalent glycemic control over the study period, but in fact the rosiglitazone group lowered their HbA1c by 0.88% relative to placebo (P < 0.001). Most patients received a statin or fibrate as lipid control medication (rosiglitazone 78%, controls 83%). Data are presented as mean ± SD. At baseline, the carotid arterial wall volume in the placebo group was 1146 ± 550 mm³and in the rosiglitazone group was 1354 ± 532 mm³. After 52 weeks, the respective volumes were 1134 ± 523 mm³and 1348 ± 531 mm³. These changes (-12.1 mm³and -5.7 mm³in the placebo and rosiglitazone groups, respectively) were not statistically significant between groups (P = 0.57).</p> <p>Conclusion</p> <p>Treatment with rosiglitazone over 1 year had no effect on progression of carotid atheroma in patients with type 2 diabetes mellitus compared to placebo.</p

Ising and Potts Models on Quenched Random Gravity Graphs

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 figure