Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormal- ization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the ' 4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the �-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormal- ization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the ' 4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the �-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.

Mar 4, 20111 citation

Optimized Perturbation Theory

Abdulla Rakhimov, Sh. Mardonov

Lecture notes in physicsJan 1, 20260 citations

Optimized Perturbation Theory: Finite Temperature Applications

Marcus Benghi Pinto

International Workshop on Relativistic Aspects of Nuclear Physics (RANP)Sep 1, 20010 citations

Power-law singularities and critical exponents in n-vector models

J. Kaupužs

Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormalization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the phi^4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the lambda-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormalization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the phi^4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the lambda-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.

arXiv:1103.0888Mar 4, 20110 citations

Field-theoretic calculation of critical exponents for the Lifshitz point

C. Mergulhão, C. E. I. Carneiro

We use field theory to calculate the critical exponents ${\ensuremath{\eta}}_{l2},$ ${\ensuremath{\eta}}_{l4},$ ${\ensuremath{\nu}}_{l2},$ and ${\ensuremath{\nu}}_{l4}$ for the Lifshitz point (LP) with $m=2$ and $m=6$ . We were motivated by an old controversy on the order ${\ensuremath{\epsilon}}^{2}$ corrections for the exponents of this multicritical point. In a previous paper, we studied the renormalization of the theory that describes the LP and derived expressions for the exponents and scaling relations that hold to all orders in perturbation. In this work we concentrate on the calculation of the Feynman diagrams that are involved in the determination of the exponents and present our results for the exponents to order ${\ensuremath{\epsilon}}^{2}.$ The evaluation of these diagrams, due to a free propagator that contains a quartic term in the momentum and is not rotationally invariant, requires special techniques that are presented in detail in the appendixes.We use field theory to calculate the critical exponents ${\ensuremath{\eta}}_{l2},$ ${\ensuremath{\eta}}_{l4},$ ${\ensuremath{\nu}}_{l2},$ and ${\ensuremath{\nu}}_{l4}$ for the Lifshitz point (LP) with $m=2$ and $m=6$. We were motivated by an old controversy on the order ${\ensuremath{\epsilon}}^{2}$ corrections for the exponents of this multicritical point. In a previous paper, we studied the renormalization of the theory that describes the LP and derived expressions for the exponents and scaling relations that hold to all orders in perturbation. In this work we concentrate on the calculation of the Feynman diagrams that are involved in the determination of the exponents and present our results for the exponents to order ${\ensuremath{\epsilon}}^{2}.$ The evaluation of these diagrams, due to a free propagator that contains a quartic term in the momentum and is not rotationally invariant, requires special techniques that are presented in detail in the appendixes.

Physical review. B, Condensed matterJun 1, 199923 citations

Convergent perturbation theory for a

Rainer Dick, A. Pollok-Narayanan, Harold C. Steinacker +1 more

The European Physical Journal CJan 1, 19990 citations

m=2

and

m=6

. We were motivated by an old controversy on the order ${\ensuremath{\epsilon}}^{2}$ corrections for the exponents of this multicritical point. In a previous paper, we studied the renormalization of the theory that describes the LP and derived expressions for the exponents and scaling relations that hold to all orders in perturbation. In this work we concentrate on the calculation of the Feynman diagrams that are involved in the determination of the exponents and present our results for the exponents to order ${\ensuremath{\epsilon}}^{2}.$ The evaluation of these diagrams, due to a free propagator that contains a quartic term in the momentum and is not rotationally invariant, requires special techniques that are presented in detail in the appendixes.