Related papers: CRITICAL (Phi^{4}_{3,\epsilon})
We prove through Monte Carlo analysis that the covariant euclidean scalar field theory, $\varphi^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ where $s$ is the spatial dimension and $1$ adds imaginary time, such…
We study the crossover between classical and nonclassical critical behaviors. The critical crossover limit is driven by the Ginzburg number G. The corresponding scaling functions are universal with respect to any possible microscopic…
We investigate the critical behaviour of the $N$-component Euclidean $\lambda \phi^4$ model at leading order in $\frac{1}{N}$-expansion. We consider it in three situations: confined between two parallel planes a distance $L$ apart from one…
We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $\phi^4$ model on the simple cubic lattice. We generalize the idea of improved models…
Given a square box $\Lambda_n\subseteq\mathbb Z^2$ of side length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\}$ with law proportional to ${\rm…
We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrability and mixing conditions, but not necessarily Gaussian. We…
The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the field $\varphi_{d}^{4}$ is obtained as a limit of regularized…
We study the one component $\Phi^4$ model for four different lattice actions in the Gaussian limit and for the Ising model in the broken phase. Emphasis is put on the euclidean invariance properties of the boson propagator. A measure of the…
The solution of the equation for the phion propagator in the leading order of the $1/N$ -- expansion for a vector-matrix model with interaction $g(\phi_a)^*\phi_b\chi_{ab}$ in four dimensions shows a change of the asymptotic behavior in the…
We consider $\phi^3$ theory in $6-2\epsilon$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $\phi$ are…
The solution of the O$(N) \phi^4$ scalar field theory in the broken phase is given in the framework of light cone quantization and a 1/N expansion. It involves the successive building of operator solutions to the equation of motion and…
We study the phase transition and critical phenomenon for the grand canonical $\Phi^3$ measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen--Fr\"ohlich--Lebowitz,…
Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the $\phi ^4$ $(4-\epsilon)$ theory is discussed. Well-known results of the asymptotic $4-\epsilon $ expansion of critical indices are shown…
We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $\beta$ functions…
Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar $\phi^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate…
Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal…
We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…
We study nonlinear cosmological perturbations and their possible non-Gaussian character in an extended non-minimal inflation where gravity is coupled non-minimally to both the scalar field and its derivatives. By expansion of the action up…
We present a simple argument which determines the critical value of the anomaly coefficient in four dimensional conformal factor quantum gravity, at which a phase transition between a smooth and elongated phase should occur. The argument is…
We focus on the behavior of (2+1)d $\lambda\phi^4$ and (5+1)d $\lambda\phi^3$ or $\lambda|\phi|^3$ theories in different regimes and compare the results obtained from the adaptive perturbation method with those obtained from lattice…