The Zero Temperature Phase Diagram of the Kitaev Model (2009)
Nash, Charles, O'Connor, Denjoe
We show that the zero temperature phase diagram of the vortex free sector of the Kitaev model is in one to one correspondence with that of the classical dimer model on the corresponding lattice. We...
Simulation of a scalar field on a fuzzy sphere (2009)
Flores, Fernando García, Martin, Xavier, O'Connor, Denjoe
The phi^4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a...
Topological Phase Transitions and Holonomies in the Dimer Model (2009)
Nash, Charles, O'Connor, Denjoe
We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be...
The Zero Temperature Phase Diagram of the Kitaev Model (2008)
Nash, Charles, O'Connor, Denjoe
We show that the zero temperature phase diagram of the vortex free sector of the Kitaev model is in one to one correspondence with that of the classical dimer model on the corresponding lattice. We...
An ab initio Calculation of the Universal Equation of State for the O(N) Model (2008)
O'Connor, Denjoe, Santiago, J. A., Stephens, C. R.
Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity...
Topological Phase Transitions and Holonomies in the Dimer Model (2008)
Nash, Charles, O'Connor, Denjoe
We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be...
Matrix Models, Gauge Theory and Emergent Geometry (2008)
Delgadillo-Blando, Rodrigo, O'Connor, Denjoe, Ydri, Badis
We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached...
Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model (2007)
Medina, Julieta, Bietenholz, Wolfgang, O'Connor, Denjoe
We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical...
Geometry in transition: A model of emergent geometry (2007)
Delgadillo-Blando, Rodrigo, O'Connor, Denjoe, Ydri, Badis
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy,...
Dolan, Brian P., Huet, Idrish, Murray, Sean, O'Connor, Denjoe
We present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms...
A Multitrace Matrix Model from Fuzzy Scalar Field Theory (2007)
O'Connor, Denjoe, Saemann, Christian
We present the analytical approach to scalar field theory on the fuzzy sphere which has been developed in arXiv:0706.2493 [hep-th]. This approach is based on considering a perturbative expansion of...
Fuzzy Scalar Field Theory as a Multitrace Matrix Model (2007)
O'Connor, Denjoe, Saemann, Christian
We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular...
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives (2006)
Dolan, Brian P., Huet, Idrish, Murray, Sean, O'Connor, Denjoe
We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of...
Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere (2006)
We find using Monte Carlo simulation the phase structure of noncommutative U(1) gauge theory in two dimensions with the fuzzy sphere S^2_N as a non-perturbative regulator. There are three phases of...
Simulating the scalar field on the fuzzy sphere (2006)
Flores, Fernando Garcia, O'Connor, Denjoe, Martin, Xavier
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are...
Field Theory Simulations on a Fuzzy Sphere - an Alternative to the Lattice (2005)
Medina, Julieta, Bietenholz, Wolfgang, Hofheinz, Frank, O'Connor, Denjoe
We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a...
The Random Walk in Generalized Quantum Theory (2004)
Martin, Xavier, O'Connor, Denjoe, Sorkin, R. D.
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical...
Fuzzy Complex Quadrics and Spheres (2003)
Dolan, Brian P., O'Connor, Denjoe, Presnajder, Peter
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension...
A Fuzzy Three Sphere and Fuzzy Tori (2003)
Dolan, Brian P., O'Connor, Denjoe
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give...
Scalar Field Theory on Fuzzy S^4 (2002)
Medina, Julieta, O'Connor, Denjoe
Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a...
Matrix models on the fuzzy sphere (2002)
Dolan, Brian P., O'Connor, Denjoe, Presnajder, Peter
Field theory on a fuzzy noncommutative sphere can be considered as a particular matrix approximation of field theory on the standard commutative sphere. We investigate from this point of view the...
Dimensional Crossover in the Non-Linear Sigma Model (2002)
O'Connor, Denjoe, Stephens, C. R., Santiago, J. A.
We consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the sigma-model limit, using ``environmentally friendly'' renormalization. We show how to...
Matrix $\phi^4$ Models on the Fuzzy Sphere and their Continuum Limits (2001)
Dolan, Brian P., O'Connor, Denjoe, Presnajder, P.
We demonstrate that the UV/IR mixing problems found recently for a scalar $\phi^4$ theory on the fuzzy sphere are localized to tadpole diagrams and can be overcome by a suitable modification of the...
Fuzzy Complex Projective Spaces and their Star-products (2001)
Balachandran, A. P., Dolan, Brian P., Lee, J., Martin, X., O'Connor, Denjoe
We derive an explicit expression for an associative *-product on fuzzy complex projective spaces. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra...
Fuzzy Actions and their Continuum Limits (2000)
Balachandran, A. P., Martin, X., O'Connor, Denjoe
Previously matrix model actions for ``fuzzy'' fields have been proposed using non-commutative geometry. They retained ``topological'' properties extremely well, being capable of describing...
Universal Scaling Properties of Superconductors in Magnetic Fields (1997)
O'Connor, Denjoe, Stephens, C. R.
Based on renormalization group arguments we establish that for a superconductor in the presence of a weak external magnetic field, $B$, the dependence on $B$ and the deviation from the critical...
Dimensional Crossover in the Large N Limit (1996)
O'Connor, Denjoe, Stephens, C. R., Bray, A. J.
We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover...
Freire, F., O'Connor, Denjoe, Stephens, C. R., Van Eijck, M. A.
$\lambda\varphi^4$ theory at finite temperature suffers from infrared divergences near the temperature at which the symmetry is restored. These divergences are handled using renormalization group...
Field Theory Entropy, the $H$-theorem and the Renormalization Group (1995)
We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of...
Modular Invariance of Finite Size Corrections and a Vortex Critical Phase (1995)
Nash, Charles, O'Connor, Denjoe
We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods $L_0$ and $L_1$ where the spins carry a representation of the fundamental group of the torus labeled by...
The Specific Heat of a Ferromagnetic Film. (1995)
Freire, F., O'Connor, Denjoe, Stephens, C. R.
We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and...
Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group (1994)
Van Eijck, M. A., O'Connor, Denjoe, Stephens, C. R.
We study $\l\f^4$ theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them...
Environmentally Friendly Renormalization in Finite-Temperature Field Theory (1994)
Van Eijck, M. A., O'Connor, Denjoe, Stephens, C. R.
Contribution to the proceedings of the NATO workshop on the Electroweak Phase Transition and the Early Universe, Sintra, March 1994. To be published by Plenum Press.
Environmentally Friendly Renormalization (1993)
O'Connor, Denjoe, Stephens, C. R.
We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are ``environment'' dependent. Relevant environmental parameters considered...
Heating Field Theory the ``Environmentally Friendly'' Way! (1993)
Van Ejick, M. A., O'Connor, Denjoe, Stephens, C. R.
We discuss how to implement an ``environmentally friendly'' renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for...
O'Connor, Denjoe, Stephens, C. R.
Series for the Wilson functions of an ``environmentally friendly'' renormalization group are computed to two loops, for an $O(N)$ vector model, in terms of the ``floating coupling'', and resummed by...
Geometry the Renormalization Group and Gravity (1993)
O'Connor, Denjoe, Stephens, C. R.
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the...