On the Divergence of Perturbation Theory: Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism

Three-dimensional Ising critical behavior in R0.6Sr0.4MnO3(R=Pr,Nd) manganites

Magnetic as well as calorimetric measurements have been performed on single crystal samples of Pr0.6Sr0.4MnO3 and Nd0.6Sr0.4MnO3 to develop a complete critical behavior study of the paramagnetic to ferromagnetic transition in both manganites. The critical exponents α,β,γ , and δ have been independently obtained. For Pr0.6Sr0.4MnO3, these are α = 0.09, β = 0.312, γ = 1.106, and δ = 4.545, while for Nd0.6Sr0.4MnO3 they are α = 0.11, β = 0.308, γ = 1.172, and δ = 4.75. All these values agree with the three-dimensional (3D)-Ising universality class (α = 0.11, β = 0.3265, γ = 1.237, and δ = 4.79) and are very far away from any other known universality class. This suggests the presence of magnetocrystalline anisotropies in the system that must be taken into account to fully describe the magnetism of these manganites, which deviates from a simple double exchange model

Critical behavior study of the spin ordering transition in RVO3 (R = Ce, Pr, Nd, Sm, Gd, Er) by means of ac photopyroelectric calorimetry

The thermal diffusivity of RVO3 single crystals (R = Ce, Pr, Nd, Sm, Gd, and Er) has been measured with an ac photopyroelectric calorimetry in the region in which the G-type orbital ordering and C-type spin ordering take place. Detailed measurements in the close neighbourhood of the spin ordering temperature have allowed to extract the critical parameter α and the critical ratio A+/A− for this transition. While the samples containing Ce, Nd, Sm and Er belong to the 3D-XY universality class (showing that the spins have an easy plane anisotropy), the sample with Gd, which is known to present a clear easy axis, belongs to the 3D-Ising class. Finally, PrVO3 shows an effective isotropic behavior, as the critical parameters found agree with the 3D-Heisenberg class

Study of the magnetocaloric effect in intermetallics RTX (R = Nd, Gd; T = Sc, Ti ; X = Si, Ge)

A detailed study of the magnetocaloric properties of six compounds of the intermetallic family RTX (R = Nd, Gd; T = Sc, Ti ; X = Si, Ge) has been undertaken: NdScSi, NdScGe, GdScSi, GdScGe, GdSc(Si0.5Ge0.5) and Gd(Sc0.5Ti0.5)Ge. The magnetic entropy changes at the Curie temperature TC and the refrigerant capacities signal that they are competitive magnetocaloric materials, showing that an improvement can be obtained by tuning the composition, as Gd(Sc0.5Ti0.5)Ge presents the best properties. These magnetocaloric variables fulfill the scaling equations with the critical parameters corresponding to the universality classes to which the ferromagnetic transitions belong (3D-XY, 3D-Heisenberg, Mean field). For each compound, a universal curve has been found for the rescaled magnetic entropy changes obtained at different applied fields, whose behavior at temperatures below TC indicate the relevance of taking into account the demagnetization field. Finally, it has been demonstrated that the rescaled magnetic entropy changes for the compounds which share the same universality class collapse onto a single universal curve.This work has been supported by Universidad del País Vasco UPV/EHU (GIU16/93)

Critical behavior of the ferromagnetic transition in GdSc(Si,Ge) intermetallic compounds

A complete study on the critical behavior of the paramagnetic to ferromagnetic transition in intermetallics GdScSi, GdScGe, GdSc(Si0.5Ge0.5) and Gd(Sc0.5Ti0.5)Ge has been carried out by means of magnetic as well as calorimetric measurements, using a high resolution ac photopyroelectric technique. The critical exponents alfa, beta, gamma, delta and the ratio of the critical coefficients A+/A- have been independently obtained for the four samples. It has been proved that the magnetic interactions are short range as the values of the critical parameters correspond to the 3D-Heisenberg class, stating an isotropic ordering of the Gd spins. In some cases, there are small deviations of some of the critical parameters from the theoretical values which have been discussed on the basis of the variation of the d states hybridization between the rare earth and the transition metal, as well as the presence of small magnetocrystalline anisotropies arising from spin-orbit coupling effects.This work has been supported by Universidad del País Vasco UPV/EHU (GIU16/93)