Spin Glass Field Theory with Replica Fourier Transforms

We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$ and the number of replica symmetry breaking steps $R$ generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any $i$-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi solution for the free-energy of an Ising spin glass.Comment: 39 pages, 3 figure

Hamilton - Jacobi treatment of front-form Schwinger model

The Hamilton-Jacobi formalism was applied to quantize the front-form Schwinger model. The importance of the surface term is discussed in detail. The BRST-anti-BRST symmetry was analyzed within Hamilton-Jacobi formalism.Comment: 11 pages, to be published in Int. Journ. Mod. Phys.

Destruction of long-range antiferromagnetic order by hole doping

We study the renormalization of the staggered magnetization of a two-dimensional antiferromagnet as a function of hole doping, in the framework of the t-J model. It is shown that the motion of holes generates decay of spin waves into ''particle-hole'' pairs, which causes the destruction of the long-range magnetic order at a small hole concentration. This effect is mainly determined by the coherent motion of holes. The value obtained for the critical hole concentration, of a few percent, is consistent with experimental data for the doped copper oxide high-Tc superconductors.Comment: 12 pages, 2 figure

Living and dying on planet Earth: an approach to the values of geodiversity

Little or no Earth Science literacy is expressed in ignorance about the close relationships between geodiversity, life, well- being, and death. However, given the environmental changes, the exponential population growth, and the predatory exploita- tion of natural resources, it is necessary to make society aware of the importance of good management of the set of geosystem services that benefit humanity, as well as the conservation of the natural resources and processes that produce these recourses. How to make society aware of the importance of Earth Sciences, geodiversity, and the services they provide? The ordering of geosystem services, following the ecosystem services model, was an important step towards launching new approaches in the teaching and popularization of geosciences. Earlier, the Big Ideas, developed under the Earth Science Literacy Initiative (ESLI), were also an important milestone to follow in the processes of teaching and popularization. Throughout this paper, topics and examples of renewable and non-renewable geologic resources and geologic processes recognized by all, but rarely understood, are suggested. Natural disasters and topics that relate to human well-being are highlighted. It is also proposed to use together the values of geodiversity identified in the scope of geosystem services and ESLI Big Ideas.This work is supported by national funding awarded by FCT- Foundation for Science and Technology, I.P., projects UIDB/04683/2020 and UIDP/04683/2020