Zygmunt Bauman’s Ethical Warnings in the Area of Economics. The Third Millennium’s Perspective

Zygmunt Bauman is not only a sociologist and philosopher reputable in the world of science, he is also a father figure for people interested in the phenomenon of globalization. Bauman investigates how current economic and political changes influence the lives of particular societies. It was important to underline that also economists can make use of Bauman’s ideas but with a few reservations That is why the following crucial areas were proposed relating to economic aspects: the meaning of consumptionism and wastage; global inequalities; the reasons and consequences of the global economic crisis, and some heterodox matters such as happiness, welfare, and well-being, all of which can be helpful in understanding the multidimensional globalization process

Dimerized ground states in spin-S frustrated systems

We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a fully dimerized ground state. This state can be exactly obtained without the need to include any additional three-body interaction in the model. The simplest members of the family can be used as a building block to generate more complex geometries like spin tubes with a fully dimerized ground state. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as the model for the description of the compound Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space where this model presents dimerization in its ground state.Comment: 10 pages, 9 figure

On the value set of small families of polynomials over a finite field, II

We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},...,a_{d-s} are fixed. Our estimate asserts that \mathcal{V}(d,s,\bfs{a})=\mu_d\,q+\mathcal{O}(q^{1/2}), where \mathcal{V}(d,s,\bfs{a}) is such an average cardinality, \mu_d:=\sum_{r=1}^d{(-1)^{r-1}}/{r!} and \bfs{a}:=(a_{d-1},...,a_{d-s}). We also prove that \mathcal{V}_2(d,s,\bfs{a})=\mu_d^2\,q^2+\mathcal{O}(q^{3/2}), where that \mathcal{V}_2(d,s,\bfs{a}) is the average second moment on any family of monic polynomials of Fq[T] of degree d with s consecutive coefficients fixed as above. Finally, we show that \mathcal{V}_2(d,0)=\mu_d^2\,q^2+\mathcal{O}(q), where \mathcal{V}_2(d,0) denotes the average second moment of all monic polynomials in Fq[T] of degree d with f(0)=0. All our estimates hold for fields of characteristic p>2 and provide explicit upper bounds for the constants underlying the \mathcal{O}--notation in terms of d and s with "good" behavior. Our approach reduces the questions to estimate the number of Fq--rational points with pairwise--distinct coordinates of a certain family of complete intersections defined over Fq. A critical point for our results is an analysis of the singular locus of the varieties under consideration, which allows to obtain rather precise estimates on the corresponding number of Fq--rational points.Comment: 36 page

Phase diagram study of a dimerized spin-S zig-zag ladder

The phase diagram of a frustrated spin-$S$ zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary $S$, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point a particular member of the family. We show that the system presents a transition between a dimerized phase to a N\'eel-like phase for $S=1/2$, and spiral phases can appear for large $S$. The phase diagram is characterized by means of a generalization of the usual Mean Field Approximation (MFA). The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the Random Phase Approximation (RPA). Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like DMRG are also presented.Comment: 14 pages, 6 figures. Some typos were corrected, and notation was clarifie