arXiv subjects

D. Johnston

Publications and source records attributed to D. Johnston.

At least 37 records · Page 2Linked to original sources

arXiv2001

Crystallization of a supercooled liquid and of a glass - Ising model approach

Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network which separate various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate dependent temperature.

cond-mat.mtrl-sci↗

arXiv2001

Wealth Condensation in Pareto Macro-Economies

We discuss a Pareto macro-economy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth and compare our results to a similar analysis in a super-open system (c) with unbounded wealth. Wealth condensation takes place in the social phase for closed and open economies, while it occurs in the liberal phase for super-open economies. In the first two cases, the condensation is related to a mechanism known from the balls-in-boxes model, while in the last case to the non-integrable tails of the Pareto distribution. For a closed macro-economy in the social phase, we point to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the total wealth is always amassed by a single individual.

cond-mat.stat-mech↗

arXiv2000

1D Potts, Yang-Lee Edges and Chaos

It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model. In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z = exp (h) plane, but their locus is still reproduced by the boundary of the chaotic region in the logistic map.

cond-mat.stat-mech↗

arXiv2000

Weak Gravitational Lensing by the Nearby Cluster Abell 3667

We present two weak lensing reconstructions of the nearby ($z_{cl}=0.055$) merging cluster Abell 3667, based on observations taken $\sim 1$ year apart under different seeing conditions. This is the lowest redshift cluster with a weak lensing mass reconstruction to date. The reproducibility of features in the two mass maps demonstrate that weak lensing studies of low-redshift clusters are feasible. These data constitute the first results from an X-ray luminosity-selected weak lensing survey of 19 low-redshift ($z< 0.1$) southern clusters.

astro-ph↗

arXiv2000

Slow dynamics of Ising models with energy barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation and aging. The addition of two-spin interactions, in general, destroys such behaviour: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

cond-mat.stat-mech↗

arXiv1999

Finite size scaling of the balls in boxes model

We discuss the finite size behaviour in the canonical ensemble of the balls in boxes model. We compare theoretical predictions and numerical results for the finite size scaling of cumulants of the energy distribution in the canonical ensemble and perform a detailed analysis of the first and third order phase transitions which appear for different parameter values in the model.

hep-lat↗

arXiv1999

Cooling-rate effects in a model of (ideal?) glass

Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model with four-spin interaction. During coarsening, this model develops growing energy barriers which at low temperature lead to very slow dynamics. We show that the characteristic zero-temperature length increases very slowly with the inverse cooling rate, similarly to the behaviour of ordinary glasses. For computationally accessible cooling rates the model undergoes an ideal glassy transition, i.e., the glassy transition for very small cooling rate coincides a thermodynamic singularity. We also study cooling of this model with a certain fraction of spins fixed. Due to such heterogeneous crystalization seeds the final state strongly depends on the cooling rate.Only for sufficiently fast cooling rate does the system end up in a glassy state while slow cooling inevitably leads to a crystal phase.

cond-mat.stat-mech↗

arXiv1999

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.

cond-mat.stat-mech↗

arXiv1999

Symmetric Vertex Models on Planar Random Graphs

We solve a 4-(bond)-vertex model on an ensemble of 3-regular Phi3 planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The method of solution, by mapping onto an Ising model in field, is inspired by the solution by Wu et.al. of the regular lattice equivalent -- a symmetric 8-vertex model on the honeycomb lattice, and also applies to higher valency bond vertex models on random graphs when the vertex weights depend only on bond numbers and not cyclic ordering (the so-called symmetric vertex models). The relations between the vertex weights and Ising model parameters in the 4-vertex model on Phi3 graphs turn out to be identical to those of the honeycomb lattice model, as is the form of the equation of the Ising critical locus for the vertex weights. A symmetry of the partition function under transformations of the vertex weights, which is fundamental to the solution in both cases, can be understood in the random graph case as a change of integration variable in the matrix integral used to define the model. Finally, we note that vertex models, such as that discussed in this paper, may have a role to play in the discretisation of Lorentzian metric quantum gravity in two dimensions.

cond-mat.stat-mech↗

arXiv1999

Weak Lensing Mass of Nearby Clusters of Galaxies

We describe first results of a project to create weak lensing mass maps for a complete, X-ray luminosity-limited sample of 19 nearby (z < 0.1) southern galaxy clusters scheduled for Sunyaev-Zel'dovich observations by the Viper Telescope at the South Pole. We have collected data on 1/3 of the sample and present motivation for the project as well as projected mass maps of two clusters.

astro-ph↗

arXiv1999

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.

hep-lat↗

arXiv1999

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.

hep-lat↗

arXiv1999

A Potts/Ising Correspondence on Thin Graphs

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reveals an isomorphism between the Potts and Ising models on thin random graphs. On planar graphs a similar correspondence is present only for q=1, the value associated with percolation.

cond-mat.stat-mech↗

arXiv1998

Phase diagram of the mean field model of simplicial gravity

We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form $p(q) = q^{-β}$, which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases~: {\em elongated} ({\em fluid}) and {\em crumpled}. For $β\in (2,\infty)$ the transition between these two phases is first order, while for $β\in (1,2]$ it is continuous. The transition becomes softer when $β$ approaches unity and eventually disappears at $β=1$. We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new {\em condensed} phase appears in the phase diagram. It bears some similarity to the {\em crinkled} phase of simplicial gravity discussed recently in models of gravity interacting with matter fields.

gr-qc↗

arXiv1998

Thin Animals

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.

cond-mat.stat-mech↗

arXiv1997

String tension in gonihedric 3D Ising models

For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare string tension is zero and the energy of a spin interface depends only on the number of bends and self-intersections, in antithesis to the standard nearest-neighbour 3D Ising action. When the parameter kappa weighting the self-intersections is small the model has a first order transition and when it is larger the transition is continuous. In this paper we investigate the scaling of the renormalized string tension, which is entirely generated by fluctuations, using Monte Carlo simulations This allows us to obtain an estimate for the critical exponents alpha and nu using both finite-size-scaling and data collapse for the scaling function.

hep-lat↗

arXiv1996

Condensation in the Backgammon model

We analyse the properties of a very simple ``balls-in-boxes'' model which can exhibit a phase transition between a fluid and a condensed phase, similar to behaviour encountered in models of random geometries in one, two and four dimensions. This model can be viewed as a generalisation of the backgammon model introduced by Ritort as an example of glassy behaviour without disorder.

cond-mat↗

arXiv1994

Random Geometries and Real Space Renormalization Group

A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration, the idea is applied to pure euclidean quantum gravity in two dimensions. Generalisation to more complicated systems and to higher dimensionalities of space-time appears straightforward.

hep-lat↗