Related papers: Symplectic critical models in $6+\epsilon$ dimensi…
Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an $Sp(N)$ invariant theory of…
We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified $D$ dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
It is conjectured that the symplectic structure of space-time is superior to the metric one. Instead of the commonly adopted pseudo-orthogonal groups SO(1,d-1), d\ge4, the complex symplectic ones Sp(2l,C), l\ge1 are proposed as the local…
The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found non-trivial fixed point in $4<d<6$ dimensions with metastable critical…
We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants,…
We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich…
We develop a method for extracting accurate critical exponents from perturbation expansions of the O(n)-symmetric nonlinear sigma-model in D=2+ epsilon dimensions. This is possible by considering the epsilon-expansions in this model as…
In this paper we study the question of determining when an irreducible admissible representation of ${\rm GL}_n(D)$ admits a symplectic model, that is when such a representation has a linear functional invariant under ${\rm Sp}_n(D)$, where…
We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits…
The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by…
We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…
We (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models…
We develop the large $D$ limit of general relativity for spherically symmetric scalar fields in both asymptotically flat and asymptotically anti-de Sitter spaces. The leading order equations in the $1/D$ expansion can be solved…
We examine anomalous dimensions of higher spin currents in the critical O(N) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories,…
We consider non-linear gravitational models with a multidimensional warped product geometry. Particular attention is payed to models with quadratic scalar curvature terms. It is shown that for certain parameter ranges, the extra dimensions…
In this thesis, we explore the critical phenomena in the presence of extended objects, which we call defects, aiming for a better understanding of the properties of non-local objects ubiquitous in our world and a more practical and…
The six-loop expansions of the renormalization-group functions of $\varphi^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4 - \varepsilon$ dimensions. The $\varepsilon$ expansions for…
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In…
We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact…