Non Perturbative Renormalization Group, momentum dependence of nn-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result

Ferrimagnetism and compensation points in a decorated 3D Ising models

We give a precise numerical solution for decorated Ising models on the simple cubic lattice which show ferromagnetism, compensation points, and reentrant behaviour. The models, consisting of $S={1\over 2}$ spins on a simple cubic lattice, and decorating S=1 or $S=3/2$ spins on the bonds, can be mapped exactly onto the normal spin-1/2 Ising model, whose properties are well known.Comment: 8 pages, 5 figure

Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_\chi=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.Comment: 11 pages, 11 figures, 14 tables. New analysis (scaling corrections in the g2=0 scenario) and new numerical simulations. Title and conclusions chang

Self-energy and critical temperature of weakly interacting bosons

Using the exact renormalization group we calculate the momentum-dependent self-energy Sigma (k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D < 4. We obtain the complete crossover function interpolating between the critical regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k) \propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the same footing with a reasonable estimate for the critical exponent eta in D=3. From our Sigma (k) we find for the interaction-induced shift of T_c in three dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density.Comment: 4 pages,1 figur

Contraceptive use and sexual function: a comparison of Italian female medical students and women attending family planning services

Objectives: The aims of the study were to understand how education relates to contraceptive choice and how sexual function can vary in relation to the use of a contraceptive method. Methods: We surveyed female medical students and women attending a family planning service (FPS) in Italy. Participants completed an online questionnaire which asked for information on sociodemographics, lifestyle, sexuality and contraceptive use and also included items of the Female Sexual Function Index (FSFI). Results: The questionnaire was completed by 413 women (362 students and 51 women attending the FPS) between the ages of 18 and 30 years. FSFI scores revealed a lower risk of sexual dysfunction among women in the control group who did not use oral hormonal contraception. The differences in FSFI total scores between the two study groups, when subdivided by the primary contraceptive method used, was statistically significant (p < 0.005). Women using the vaginal ring had the lowest risk of sexual dysfunction, compared with all other women, and had a positive sexual function profile. In particular, the highest FSFI domain scores were lubrication, orgasm and satisfaction, also among the control group. Expensive contraception, such as long-acting reversible contraception, was not preferred by this young population, even though such methods are more contemporary and manageable. Compared with controls, students had lower compliance with contraception and a negative attitude towards voluntary termination of pregnancy. Conclusion: Despite their scientific knowledge, Italian female medical students were found to need sexual and contraceptive assistance. A woman's sexual function responds to her awareness of her body and varies in relation to how she is guided in her contraceptive choice. Contraceptive counselling is an excellent means to improve female sexuality

Towards a fully automated computation of RG-functions for the 3-dd O(N) vector model: Parametrizing amplitudes

Within the framework of field-theoretical description of second-order phase transitions via the 3-dimensional O(N) vector model, accurate predictions for critical exponents can be obtained from (resummation of) the perturbative series of Renormalization-Group functions, which are in turn derived --following Parisi's approach-- from the expansions of appropriate field correlators evaluated at zero external momenta. Such a technique was fully exploited 30 years ago in two seminal works of Baker, Nickel, Green and Meiron, which lead to the knowledge of the $\beta$-function up to the 6-loop level; they succeeded in obtaining a precise numerical evaluation of all needed Feynman amplitudes in momentum space by lowering the dimensionalities of each integration with a cleverly arranged set of computational simplifications. In fact, extending this computation is not straightforward, due both to the factorial proliferation of relevant diagrams and the increasing dimensionality of their associated integrals; in any case, this task can be reasonably carried on only in the framework of an automated environment. On the road towards the creation of such an environment, we here show how a strategy closely inspired by that of Nickel and coworkers can be stated in algorithmic form, and successfully implemented on the computer. As an application, we plot the minimized distributions of residual integrations for the sets of diagrams needed to obtain RG-functions to the full 7-loop level; they represent a good evaluation of the computational effort which will be required to improve the currently available estimates of critical exponents.Comment: 54 pages, 17 figures and 4 table

New Optimization Methods for Converging Perturbative Series with a Field Cutoff

We take advantage of the fact that in lambda phi ^4 problems a large field cutoff phi_max makes perturbative series converge toward values exponentially close to the exact values, to make optimal choices of phi_max. For perturbative series terminated at even order, it is in principle possible to adjust phi_max in order to obtain the exact result. For perturbative series terminated at odd order, the error can only be minimized. It is however possible to introduce a mass shift in order to obtain the exact result. We discuss weak and strong coupling methods to determine the unknown parameters. The numerical calculations in this article have been performed with a simple integral with one variable. We give arguments indicating that the qualitative features observed should extend to quantum mechanics and quantum field theory. We found that optimization at even order is more efficient that at odd order. We compare our methods with the linear delta-expansion (LDE) (combined with the principle of minimal sensitivity) which provides an upper envelope of for the accuracy curves of various Pade and Pade-Borel approximants. Our optimization method performs better than the LDE at strong and intermediate coupling, but not at weak coupling where it appears less robust and subject to further improvements. We also show that it is possible to fix the arbitrary parameter appearing in the LDE using the strong coupling expansion, in order to get accuracies comparable to ours.Comment: 10 pages, 16 figures, uses revtex; minor typos corrected, refs. adde

Critical renormalized coupling constants in the symmetric phase of the Ising models

Using a novel finite size scaling Monte Carlo method, we calculate the four, six and eight point renormalized coupling constants defined at zero momentum in the symmetric phase of the three dimensional Ising system. The results of the 2D Ising system that were directly measured are also reported. Our values of the six and eight point coupling constants are significantly different from those obtained from other methods.Comment: 7 pages, 2 figure

Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation, gives results which stay close to the exact solution for longer than previous methods. It provides a promising basis for extension to a full field theoretic treatment.Comment: 12 pages, including 4 figure