arXiv subjects

J. F. Wheater

Publications and source records attributed to J. F. Wheater.

13 recordsLinked to original sources

arXiv2014

A restricted dimer model on a 2-dimensional random causal triangulation

We introduce a restricted hard dimer model on a random causal triangulation that is exactly solvable and generalizes a model recently proposed by Atkin and Zohren. We show that the latter model exhibits unusual behaviour at its multicritical point; in particular, its Hausdorff dimension equals 3 and not 3/2 as would be expected from general scaling arguments. When viewed as a special case of the generalized model introduced here we show that this behaviour is not generic and therefore is not likely to represent the true behaviour of the full dimer model on a random causal triangulation.

hep-th↗

arXiv2003

Symmetries in QFT

This document contains notes from the graduate lecture course, "Symmetries in QFT" given by J.F.Wheater at Oxford University in Hilary term. The course gives an informal introduction to QFT.

hep-ph↗

arXiv2002

Rotational Symmetry Breaking in Multi-Matrix Models

We consider a class of multi-matrix models with an action which is O(D) invariant, where D is the number of NxN Hermitian matrices X_μ, μ=1,...,D. The action is a function of all the elementary symmetric functions of the matrix $T_{μν}=Tr(X_μX_ν)/N$. We address the issue whether the O(D) symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the O(D) symmetry is maximally broken.

hep-th↗

arXiv1996

A simple model of dimensional collapse

We consider a simple model of d families of scalar field interacting with geometry in two dimensions. The geometry is locally flat and has only global degrees of freedom. When d<0 the universe is locally two dimensional but for d>0 it collapses to a one dimensional manifold. The model has some, but not all, of the characteristics believed to be features of the full theory of conformal matter interacting with quantum gravity which has local geometric degrees of freedom.

hep-th↗

arXiv1996

Avalanche size distribution in a random walk model

We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches and other self-organized critical phenomena in one dimension. We find scaling laws relating the frequency, size and width of avalanches and an exponent $4/3$ in the size distribution law.

cond-mat↗

arXiv1996

Critical properties of the Z(3) interface in (2+1)-D SU(3) gauge theory

We study the interface between two different Z(3) vacua in the deconfined phase of SU(3) pure gauge theory in 2+1 dimensions just above the critical temperature. In simulations of the Euclidean lattice gauge theory formulation of the system we measure the fluctuations of the interface as the critical temperature is approached and as a function of system size. We show that the intrinsic width of the interface remains small even very close to the critical temperature. Some dynamical exponents which govern the interaction of the interface with our Monte Carlo algorithm are also estimated. We conclude that the Z(3) interface has properties broadly similar to those in many other comparable statistical mechanical systems.

hep-lat↗

arXiv1996

High-Temperature Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge Theory

We study the high-temperature properties of the Z(3) interface which forms between the various ordered phases of pure SU(3) gauge theory above a critical temperature. On a (2+1)-D Euclidean lattice, we perform an accurate measurement of the interface tension, which shows good agreement with the prediction of perturbation theory. We also examine the behaviour of the Debye electric screening mass, and compare this with theoretical predictions.

hep-lat↗

arXiv1995

Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge Theory

A study is made of some properties of this interface in the SU(3) pure gauge theory in 2+1 dimensions. At high temperatures, the interface tension is measured and shows agreement with the perturbative prediction. Near the critical temperature, the behaviour of the interface is examined, and its fluctuations compared to a scalar field theory model.

hep-lat↗

arXiv1995

The Critical Exponents of Crystalline Random Surfaces

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be $ν=0.71(5)$ from the tangent-tangent correlation function whereas we find $ν=0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $α=0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a $χ^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $α$. Our measurements of the normal-normal correlation functions suggest that the model in the crumpled phase is described by an effective field theory which deviates from a free field theory only by super-renormalizable interactions.

hep-lat↗

arXiv1994

The phase diagram of an Ising model on a polymerized random surface

We construct a random surface model with a string susceptibility exponent one quarter by taking an Ising model on a random surface and introducing an additional degree of freedom which amounts to allowing certain outgrowths on the surfaces. Fine tuning the Ising temperature and the weight factor for outgrowths we find a triple point where the susceptibility exponent is one quarter. At this point magnetized and nonmagnetized gravity phases meet a branched polymer phase.

hep-th↗

arXiv1994

Multiple Ising Spins Coupled to 2d Quantum Gravity

We study a model in which p independent Ising spins are coupled to 2d quantum gravity (in the form of dynamical planar phi-cubed graphs). Consideration is given to the p tends to infinity limit in which the partition function becomes dominated by certain graphs; we identify most of these graphs. A truncated model is solved exactly providing information about the behaviour of the full model in the limit of small beta. Finally, we derive a bound for the critical value of the coupling constant, beta_c and examine the magnetization transition in the limit p tends to zero.

hep-th↗

arXiv1993

On the Transition from Crystalline to Dynamically Triangulated Surfaces

We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an alternative based on Alexander moves. Two simplified models, one of which has a phase transition and the other of which does not, are discussed.

hep-lat↗

arXiv1993

On the Crumpling Transition in Crystalline Random Surfaces

We investigate the crumpling transition on crystalline random surfaces with extrinsic curvature on lattices up to $64^2$. Our data are consistent with a second order phase transition and we find correlation length critical exponent $ν=0.89\pm 0.07$. The specific heat exponent, $α=0.2\pm 0.15$, is in much better agreement with hyperscaling than hitherto. The long distance behaviour of tangent-tangent correlation functions confirms that the so-called Hausdorff dimension is $d_H=\infty$ throughout the crumpled phase.

hep-lat↗