Editorial

1999

Phys. Rev. D

The optimized linear δ-expansion is applied to the λφ 4 theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order δ 2 . A variational procedure associated with the method generates nonperturbative results which are used to obtain the critical temperature for the phase transition. Our results are compared with the ones given by propagator dressing methods.

Section: A the Linear δ-Expansionmentioning

confidence: 84%

High temperature resummation in the linearδexpansion

Pinto

1999

Phys. Rev. D

“…[13]. However, they made use of the nonlinear version of method which leads to a considerable more complicated perturbation series (see also [14]), which quickly becomes cumbersome beyond leading order in δ and their results were not so good for the same critical exponents evaluated here. On the other hand, the way the linear version is employed here avoids those difficulties and the results can in principle be extended to arbitrary orders as usual perturbative calculations.…”

Section: Introductionmentioning

confidence: 99%

Evaluating critical exponents in the optimized perturbation theory

Pinto

Physica A: Statistical Mechanics and its Applications

Sena

2004

We use the optimized perturbation theory, or linear δ expansion, to evaluate the critical exponents in the critical 3d O(N ) invariant scalar field model. Regarding the implementation procedure, this is the first successful attempt to use the method in this type of evaluation. We present and discuss all the associated subtleties producing a prescription which can, in principle, be extended to higher orders in a consistent way. Numerically, our approach, taken at the lowest nontrivial order (second order) in the δ expansion produces a modest improvement in comparison to mean field values for the anomalous dimension η and correlation length ν critical exponents. However, it nevertheless points to the right direction of the values obtained with other methods, like the ǫ-expansion. We discuss the possibilities of improving over our lowest order results and on the convergence to the known values when extending the method to higher orders.

A NONEQUILIBRIUM STATISTICAL ENSEMBLE FORMALISM MaxEnt–NESOM: Basic Concepts, Construction, Application, Open Questions and Criticisms

Luzzi

Vasconcellos

2000

Int. J. Mod. Phys. B

Self Cite

We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the seminal and fundamental ideas set forward by Boltzmann and Gibbs. The existing approaches can be unified under a unique variational principle, namely, MaxEnt, which we consider here. The main six basic steps that are at the foundations of the formalism are presented and the fundamental concepts are discussed. The associated nonlinear quantum kinetic theory and the accompanying Statistical Thermodynamics (the Informational Statistical Thermodynamics) are very briefly described. The corresponding response function theory for systems away from equilibrium allows to connected the theory with experiments, and some examples are summarized; there follows a good agreement between theory and experimental data in the cases in which the latter are presently available. We also present an overview of some conceptual questions and associated criticisms.