We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of q-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a nontrivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle, which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent alpha of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of q). The critical exponents do not depend on the strengths of the exchange interactions.

We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, the uniform fixed point in the parameter space becomes fully unstable. We analyze some limiting cases, and propose a heuristic criterion to check the relevance of the fluctuations.

We write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuations.

We review and extend some recent investigations of the effects of aperiodic interactions on the critical behavior of ferromagnetic $q$-state Potts models. By considering suitable diamond or necklace hierarchical lattices, and assuming a distribution of interactions according to a class of two-letter substitution rules, the problem can be formulated in terms of recursion relations in parameter space. The analysis of stability of the fixed points leads to an exact criterion to gauge the relevance of geometric fluctuations. For irrelevant fluctuations, the critical behavior remains unchanged with respect to the uniform systems. For relevant fluctuations, there appears a two-cycle of saddle-point character in parameter space. A scaling analysis, supported by direct numerical thermodynamic calculations, shows the existence of novel critical universality classes associated with relevant geometric fluctuations. Also, we show that similar qualitative results are displayed by a simple model of two directed polymers on a diamond hierarchical structure with aperiodic bond interactions.Comment: 3 eps figures (included). Invited talk in STATPHYS21, proceedings to be published in Physica

Após trabalhar em Sevilha e Lisboa por alguns anos, o holandês Jan Huygen van Linschoten (c. 1563-1611) foi nomeado guarda-livros e secretário do recém-indicado arcebispo de Goa, o dominicano Vicente da Fonseca, em 1583. Ao retornar à Europa quase uma década depois, tendo vivido em Goa por mais de cinco anos, Linschoten começou a publicar relatos de viagem e instruções náuticas que encontraram extraordinário sucesso. Sua principal publicação, o Itinerario, foi editada em holandês por Cornelis Claesz em 1596 (com uma cópia avançada tendo sido entregue um ano antes à primeira frota holandesa que navegou para as Índias Orientais), e quase imediatamente traduzida para o inglês (1598) por sugestão de Richard Hakluyt, que recomendou o livro à Companhia das Índias Orientais da Inglaterra. Edições em latim, alemão e francês logo se seguiram. Sua extensa circulação e as valiosas instruções de navegação que continha fizeram dele um dos livros que mais propagaram o conhecimento sobre o Estado português da Índia pela Europa, tendo tido impacto direto sobre as empresas holandesas, britânicas, francesas e dinamarquesas rumo à Ásia. Além de um relato de viagem e compêndio da história natural indiana, o Itinerario também é uma longa meditação moral sobre os modos e atitudes dos portugueses em relação aos habitantes de Goa – sua “etnografia implícita” – e sobre sua falência em manter uma distância segura em relação a eles, o que representa uma avaliação negativa do próprio sistema de “conhecimento colonial” dos portugueses.