Related papers: Simulating the scalar field on the fuzzy sphere
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 disordered phase, and a non-uniform ordered…
The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is…
The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These…
The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for…
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 scalar $\phi^4$ theory. We demonstrate that…
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…
We propose a new algorithm for simulating noncommutative phi-four theory on the fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field, in such a way that in the commutative limit N\longrightarrow \infty, the two modes…
We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
We study the phase diagram of the scalar field theory on the fuzzy sphere described as a particular multitrace matrix model. We consider perturbative and nonperturbative terms in the kinetic term effective action and describe consequences…
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 fuzzy sphere with radius R for the two…
We study the phase structure of the scalar field theory on fuzzy $\mathbb C P^n$ in the large $N$ limit. Considering the theory as a hermitian matrix model we compute the perturbative expansion of the kinetic term effective action under the…
We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of…
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram…
We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between…
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 harmonics. This yields a numerically…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
Scalar field theory on the fuzzy two-sphere, represented as a hermitian matrix model that includes kinetic, mass and quartic interaction terms, is studied. The effective action in the symmetric large-N regime is analyzed using a…
We study renormalization on the fuzzy sphere, which is a typical example of non-commutative spaces. We numerically simulate a scalar field theory on the fuzzy sphere, which is described by a Hermitian matrix model. We define correlation…
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 the model. i) A matrix phase where the…