Abstract:
The Ashkin-Teller model can be formulated as a pair of 2D Ising models, interacting via a four-spin interaction. I consider the case of weak anisotropy (slight a-symmetry between the two Ising layers) and weak coupling. I show that the system admits two critical temperatures whose difference varies continuously with the strength of the coupling, scaling with an anomalous exponent as one let the a-symmetry parameter go to zero. The specific heat diverges logarithmically at the critical points (as for Ising) but the constant in front of the logarithm is renormalized by an anomalous critical exponent. The logarithmic divergence of the specific heat dominates only in an exponentially small interval around the critical temperatures and outside it is modified into an anomalous power law behaviour. The proof is based on an exact mapping of Ashkin-Teller into a model of (1+1)D interacting fermions and on the implementation of constructive Renormalization group methods on the fermionic system. This PhD thesis includes: (1) a review of the exact solution of 2D Ising in terms of Grassmann functional integrals; (2) a review of the Grassmann representation for a class of interacting Ising models, including Ashkin-Teller and the 8 vertex model; (3) a detailed discussion of the multiscale analysis of the Ashkin-Teller model, based on fermionic Renormalization Group methods, including the study of the flow of the effective coupling constants (in particular a proof of vanishing of the beta function for this and similar Luttinger-like models, based on modified approximate Ward identities, is included). This thesis is based on joint work with V. Mastropietro.

Abstract:
El presente trabajo propone un recorrido sobre las principales teorías de las emociones y la regulación emocional, haciendo especial hincapié en las propuestas específicas para adultos mayores. El marco organizador es la teoría del curso vital, ya que permite integrar los aportes tomando como eje los distintos tipos de influencias que intervienen en el desarrollo humano. Se revisan las teorías psicobiológicas, sociológicas e integradoras de la emoción, así como los constructos de mecanismos de defensa, apego y afrontamiento emocional, seleccionados por su estrecha relación con la regulación de las emociones. Posteriormente, se aborda el constructo de inteligencia emocional y dos propuestas para el estudio de la regulación de las emociones en adultos mayores. Se realiza un comentario integrador, focalizando en los puntos comunes entre los conceptos presentados, resaltando el vínculo entre las emociones y las relaciones interpersonales. Las miradas integrales son de particular importancia en la vejez, ya que es una etapa vital que se caracteriza por un alto nivel de heterogeneidad y, por lo tanto, representa un desafío para la comprensión de investigadores y profesionales de la salud mental.

Abstract:
We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when the isotropic limit is reached. We prove that, even in the region where universality for the specific heat holds, anomalous critical exponents appear: for instance we predict the existence of a previously unknown anomalous exponent, continuously varying with the strength of the interaction, describing how the difference between the critical temperatures rescales with the anisotropy parameter.

Abstract:
The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescales with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.

Abstract:
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting bosons (magnons). We prove this fact at the level of the specific free energy: if $ S \to \infty $ and the inverse temperature $ \beta \to 0 $ in such a way that $ \beta S $ stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof is based on the localization of the system in small boxes and on upper and lower bounds on the local free energy, and it also provides explicit error bounds on the remainder.

Abstract:
We examine the current directions in the search for spin-dependent dark matter. We discover that, with few exceptions, the search activity is concentrated towards constraints on the WIMP-neutron spin coupling, with significantly less impact in the WIMP-proton sector. We review the situation of those experiments with WIMP-proton spin sensitivity, toward identifying those capable of reestablishing the balance.

Abstract:
This paper reports about an approach to the classification of proteins' primary structures taking advantage of the Self Organizing Maps algorithm and of a numerical coding of the aminoacids based upon their physico-chemical properties. Hydrophobicity, volume, surface area, hydrophilicity, bulkiness, refractivity and polarity were subjected to a Principal Component Analysis and the first two principal components, explaining 84.8 % of the total observed variability, were used to cluster the aminoacids into 4 or 5 classes through a k-means algorithm. This leads to an economical representation of the primary structures which, in the construction of the input vectors for the Self Organizing Maps algorithm, allows the consideration of up to tri- and tetrapeptides' frequency matrices with minimal computational overload. In comparison with previously explored conditions, namely symbolic coding of aminoacids and dipeptides frequencies, no significant improvement was observed in the classification of 69 cytochromes of the c type, characterized by a high degree of structural and functional similarity, while a substantial improvement occurred in the case of a data set including quite heterogeneous primary structures.

Abstract:
We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.

Abstract:
We explore the properties of the Barcelona Catania Paris Madrid (BCPM) energy density functional concerning fission dynamics. Potential energy surfaces as well as collective inertias relevant in the fission process are computed for several nuclei where experimental data exists. Inner and outer barrier heights as well as fission isomer excitation energies are reproduced quite well in all the cases. The spontaneous fission half lives $t_{\textrm{\textrm{SF}}}$ are also computed using the standard semiclassical approach and the results are compared with the experimental data. A reasonable agreement with experiment is found over a range of 27 orders of magnitude but the theoretical predictions suffer from large uncertainties associated to the values of the parameters entering the spontaneous fission half life formula. The impact that increasing the pairing correlations strengths has in the spontaneous fission half lives is analyzed and found to be large in all the nuclei considered. Given the satisfactory description of the trend of fission properties with mass number we explore the fission properties of the even-even uranium isotope chain from $^{226}$U to $^{282}$U. Very large half lives are found when getting close to neutron number N=184.