Related papers: Dimensional Crossover and Effective Exponents
Effective critical exponents for the \lambda \phi^4 scalar field theory are calculated as a function of the renormalization group block size k_o^{-1} and inverse critical temperature \beta_c. Exact renormalization group equations are…
Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambda phi^4 model with external source and without mass and they have clarified that there are underlying renormalization group structure, including the phenomenon of the…
We calculate the explicit expression of the effective potential in a $\lambda\phi^4$ theory at finite temperature in a static universe for arbitrary spacetime dimensions (2\leq D < 5). To study the combined effects of the temperature and…
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 derive critical temperature shifts, giving…
The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of…
We investigate the critical behavior that d-dimensional systems with short-range forces and a n-component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in a m-dimensional isotropic subspace of ${\mathbb…
We consider the massive vector $N$-component $(\lambda\phi^{4})_{D}$ theory in Euclidian space and, using an extended Matsubara formalism we perform a compactification on a $d$-dimensional subspace, $d\leq D$. This allows us to treat…
Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an…
In this paper, we study in details the critical behavior of the ${\cal O}(n)$ quantum $\phi^4$ model with long-range interaction decaying with the distances r by a power law as $r^{-d-\sigma}$ in the large n-limit. The zero-temperature…
Using the Matsubara formalism, we consider the massive $(\lambda \phi^{4})_{D}$ vector $N$-component model in the large $N$ limit, the system being confined between two infinite paralell planes. We investigate the behavior of the coupling…
We present a detailed version of our recent work on the renormalization group approach to multicritical scalar theories with higher derivative kinetic term of the form $\phi(-\Box)^k\phi$ and upper critical dimension $d_c = 2nk/(n-1)$.…
A fundamental issue in the renormalization-group (RG) theory of critical phenomena concerns the allowed values of critical exponents that are consistent with the continuous nature of a phase transition. Here we conjecture a lower bound for…
We observe that probing certain classical field theories by external sources uncovers the underlying renormalization group structure, including the phenomenon of dimensional transmutation, at purely-classical level. We perform this study on…
The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+\sigma}$, $\sigma>0$. The attention is focused mainly on the renormalization group…
We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi_{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{1 +…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
We report on the progress in the computation of the beta-functions of phi^4 theory and QCD in the large N expansion. For the former we give an analytic formula for the critical exponent which encodes higher order coefficients in the series…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, are investigated. The system is confined to a…
We study the phase diagram of the four dimensional O(4) model with first (beta1) and second (beta2) neighbor couplings, specially in the beta2 < 0 region, where we find a line of transitions which seems to be second order. We also compute…