Related papers: Phase diagram and dispersion relation of the non-c…
We present a numerical study of the \lambda \phi^{4} model in three Euclidean dimensions, where the two spatial coordinates are non-commutative (NC). We first show the explicit phase diagram of this model on a lattice. The ordered regime…
In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present…
We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase…
We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where…
The UV/IR mixing in the \lambda \phi^4 model on a non-commutative (NC) space leads to new predictions in perturbation theory, including Hartree-Fock type approximations. Among them there is a changed phase diagram and an unusual behavior of…
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of R^{2n}_\theta…
We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally…
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 study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…
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 spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in…
We show that the spectrum of the three dimensional phi^4 theory in the broken symmetry phase contains non-perturbative states. We determine the spectrum using a new variational technique based on the introduction of operators corresponding…
We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field…
It is pointed out that one-component \phi^4 lattice theory in four dimensions has a non-perturbative sector which can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a…
A fermion model with random on-site potential defined on a two-dimensional square lattice with $\pi$-flux is studied. The continuum limit of the model near the zero energy yields Dirac fermions with random potentials specified by four…
The 2d gauge theory on the lattice is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point…
A time dependent variational approach is considered to derive the equations of movement for the $\lambda \phi^4$ model. The temporal evolution of the model is performed numerically in the frame of the Gaussian approximation in a lattice of…
In the work, we investigated a generalized model of the fermionic lattice gas in the form of the extended Hubbard model with intersite Ising-like interactions (both antiferromagnetic and ferromagnetic) at the atomic limit on the triangular…
The one-component $\lambda\phi^4$ theory in four dimensions in the spontaneously broken symmetry phase has a non-trivial, non-perturbative sector which can be studied by means of a duality transformation of its Ising limit. Duality maps…
The leading-order equations of the $1/N$ -- expansion for a vector-matrix model with interaction $g\phi_a^*\phi_b\chi_{ab}$ in four dimensions are investigated. This investigation shows a change of the asymptotic behavior in the deep…