Related papers: Renormalization and resummation in the O(N) model
We construct a functional renormalisation group for thermal fluctuations. Thermal resummations are naturally built in, and the infrared problem of thermal fluctuations is well under control. The viability of the approach is exemplified for…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
Well-known and newly developed renormalization schemes for $\tan\beta$ are analyzed in view of three desirable properties: gauge independence, process independence, and numerical stability in perturbation theory. Arguments are provided that…
We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the…
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a…
Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the…
Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon…
We examine the issue of renormalizability of asymptotically free field theories on non-commutative spaces. As an example, we solve the non-commutative O(N) invariant Gross-Neveu model at large N. On commutative space this is a…
The first renormalization group map arising from the momentum space decomposition of a weakly coupled system of fermions at temperature zero differs from all subsequent maps. Namely, the component of momentum dual to temperature may be…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
The renormalization of a gapless Phi-derivable Hartree--Fock approximation to the O(N)-symmetric lambda*phi^4 theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper in…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
We apply analytic perturbation theory in next-to-next-to-leading order to inclusive semileptonic $\tau$-decay and study the renormalization scheme dependence. We argue that the renormalization scheme ambiguity is considerably reduced in the…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…