Related papers: Finite Size Effects in the Anisotropic \lambda/4!(…

The equilibrium statistical mechanics of a d dimensional ``oriented'' manifold in an N+d dimensional random medium are analyzed in d=4-epsilon dimensions. For N=1, this problem describes an interface pinned by impurities. For d=1, the model…

We study symmetry-breaking line defects in the Wilson-Fisher theory with $O(2N+1)$ global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with $O(2N)$ global symmetry near six dimensions. We introduce…

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x L lattice in 3D) is transmuted to 1/L^2 scaling if there is an exponential low-temperature…

This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Corrections On Random Graphs; Chapter 5 - The Random Field Ising…

We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>, where Phi…

There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using the functional renormalization group equation, we show that in the lowest order of the…

In this paper we give a much more efficient proof that the real Euclidean phi 4-model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator which complete the previous…

We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by…

The Ewald3D sum with the tinfoil boundary condition (e3dtf) evaluates the electrostatic energy of a finite unit cell inside an infinitely periodic supercell. Although it has been used as a {\it de facto} standard treatment of electrostatics…

We analyze the critical line of $\lambda\phi^4_4$ perturbatively in the bare coupling $\lambda_0$, by setting the daisy-improved renormalized mass to zero. By comparing to lattice data, we can then quantify the relation between the…

We consider the 2PI Cornwall-Jackiw-Tomboulis effective action at finite temperature for a noncommutative real scalar field theory in 4 dimensions, with noncommutativity among space and time variables. By means of a Rayleig-Ritz variation,…

We consider paramagnetic, spin-glass and ferromagnetic phases. At $T=0$ model gives for the some values of connectivity (near the critical) extremal suppression of finite size effects (decoding error probability).

The first goal of this paper is to study necessary and sufficient conditions to obtain the attainability of the \textit{fractional Hardy inequality } $$\Lambda_{N}\equiv\Lambda_{N}(\Omega):=\inf_{\{\phi\in \mathbb{E}^s(\Omega, D), \phi\neq…

The out-of-equilibrium dynamics of the O(N+1) nonlinear sigma model in 1+1 dimensions is investigated in the large N limit. Regarding the nonlinearity as the effect of a suitable large coupling limit of the O(N+1) \phi^4 model, we first of…

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…

We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet,…

We consider the fourth-order nonlinear elliptic problem: \begin{equation*} \begin{array}{ll} \Delta(a(x)\Delta u) = a(x) \left\vert u \right\vert^{p-2-\epsilon} u \ \text{ in } \ \Omega, \hspace{0.6cm} u = 0 \ \text{ on } \ \partial \Omega,…

Unconditionally, we prove the Iwaniec-Sarnak conjecture for $L^4$-norms of the Hecke-Maass cusp forms. From this result, we can justify that for even Maass cusp form $\phi$ with the eigenvalue $\lambda_{\phi}=\frac{1}{4}+t_{\phi}^2$, for…

A suitable counterterm for a Euclidean space lattice version of \phi^4_n theories, n\ge 4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support…

In this paper we shall study whether dissipation in a $\lambda\phi^{4}$ may be described, in the long wavelength, low frequency limit, with a simple Ohmic term $\kappa\dot{\phi}$, as it is usually done, for example, in studies of defect…