Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields

The behavior of the nonlinear susceptibility $\chi_3$ and its relation to the spin-glass transition temperature $T_f$, in the presence of random fields, are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue $\lambda_{\rm AT}$ (replicon) on the random fields is analyzed. Particularly, in absence of random fields, the temperature $T_f$ can be traced by a divergence in the spin-glass susceptibility $\chi_{\rm SG}$, which presents a term inversely proportional to the replicon $\lambda_{\rm AT}$. As a result of a relation between $\chi_{\rm SG}$ and $\chi_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of $\lambda_{\rm AT}=0$ at $T_f$. However, our results show that, in the presence of random fields, $\chi_3$ presents a rounded maximum at a temperature $T^{*}$, which does not coincide with the spin-glass transition temperature $T_f$ (i.e., $T^* > T_f$ for a given applied random field). Thus, the maximum value of $\chi_3$ at $T^*$ reflects the effects of the random fields in the paramagnetic phase, instead of the non-trivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that $\chi_3$ still maintains a dependence on the replicon $\lambda_{\rm AT}$, although in a more complicated way, as compared with the case without random fields. These results are discussed in view of recent observations in the LiHo$_x$Y$_{1-x}$F$_4$ compound.Comment: accepted for publication in PR

Towards an optical potential for rare-earths through coupled channels

The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations, defined by nuclear deformations. Proper treatment of such excitations is often essential to the accurate description of reaction experimental data. Previous works have applied different models to specific nuclei with the purpose of determining angular-integrated cross sections. In this work, we present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. Inspired by the work done by Dietrich \emph{et al.}, a model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed. We demonstrate that the obtained results of calculations for total, elastic and inelastic cross sections, as well as elastic and inelastic angular distributions correspond to a remarkably good agreement with experimental data for scattering energies above around a few MeV.Comment: 7 pages, 6 figures. Submitted to the proceedings of the XXXVI Reuni\~ao de Trabalho de F\'{\i}sica Nuclear no Brasil (XXXVI Brazilian Workshop on Nuclear Physics), held in Maresias, S\~ao Paulo, Brazil in September 2013, which should be published on AIP Conference Proceeding Series. arXiv admin note: substantial text overlap with arXiv:1311.1115, arXiv:1311.042

Reaction cross-section predictions for nucleon induced reactions

A microscopic calculation of the optical potential for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all the particle-hole (p-h) excitation states in the target and to all relevant pickup channels. These p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and to long-lived compound nucleus resonances. We calculated the reaction cross sections for the nucleon induced reactions on the targets $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm using the QRPA description of target excitations, coupling to all inelastic open channels, and coupling to all transfer channels corresponding to the formation of a deuteron. The results of such calculations were compared to predictions of a well-established optical potential and with experimental data, reaching very good agreement. The inclusion of couplings to pickup channels were an important contribution to the absorption. For the first time, calculations of excitations account for all of the observed reaction cross-sections, at least for incident energies above 10 MeV.Comment: 6 pages, 6 figures. Submitted to INPC 2010 Conference Proceeding

Multispecies effects in the equilibrium and out-of-equilibrium thermostatistics of overdamped motion

Progress has been recently made, both theoretical and experimental, regarding the thermostatistics of complex systems of interacting particles or agents (species) obeying a nonlinear Fokker-Planck dynamics. However, major advances along these lines have been restricted to systems consisting of only one type of species. The aim of the present contribution is to overcome that limitation, going beyond single-species scenarios. We investigate the dynamics of overdamped motion in interacting and confined many-body systems having two or more species that experience different intra- A nd interspecific forces in a regime where forces arising from standard thermal noise can be neglected. Even though these forces are neglected, the behavior of the system can be analyzed in terms of an appropriate thermostatistical formalism. By recourse to a mean-field treatment, we derive a set of coupled nonlinear Fokker-Planck equations governing the behavior of these systems. We obtain an H theorem for this Fokker-Planck dynamics and discuss in detail an example admitting an exact, analytical stationary solution.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nobre, F. D.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Wedemann, R. S.. Universidade do Estado de Rio do Janeiro; Brasi

Stochastic Perturbations in Vortex Tube Dynamics

A dual lattice vortex formulation of homogeneous turbulence is developed, within the Martin-Siggia-Rose field theoretical approach. It consists of a generalization of the usual dipole version of the Navier-Stokes equations, known to hold in the limit of vanishing external forcing. We investigate, as a straightforward application of our formalism, the dynamics of closed vortex tubes, randomly stirred at large length scales by gaussian stochastic forces. We find that besides the usual self-induced propagation, the vortex tube evolution may be effectively modeled through the introduction of an additional white-noise correlated velocity field background. The resulting phenomenological picture is closely related to observations previously reported from a wavelet decomposition analysis of turbulent flow configurations.Comment: 16 pages + 2 eps figures, REVTeX