An Introduction to the Theory of Spin Glasses

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method, and the dynamical mean-field theory. In the second part, we deal with the description of low-dimensional systems, mostly in three spatial dimensions, which are mostly studied through numerical simulations. We conclude by mentioning some of the main open problems in the field.Comment: To appear as a chapter of the "Encyclopedia of Condensed Matter Physics", 2nd edition (Elsevier

Precursors of the Spin Glass Transition in Three Dimensions

We study energy landscape and dynamics of the three-dimensional Heisenberg Spin Glass model in the paramagnetic phase, i.e. for temperature $T$ larger than the critical temperature $T_\mathrm{c}$. The landscape is non-trivially related to the equilibrium states even in the high-temperature phase, and reveals an onset of non-trivial behavior at a temperature $T_\mathrm{o}$, which is also seen through the behavior of the thermoremanent magnetization. We also find a power-law growth of the relaxation times far from the spin-glass transition, indicating a dynamical crossover at a temperature $T_\mathrm{d}$, $T_\mathrm{c}<T_\mathrm{d}<T_\mathrm{o}$. The arising picture is reminiscent of the phenomenology of supercooled liquids, and poses questions on which mean-field models can describe qualitatively well the phenomenology in three dimensions. On the technical side, local energy minima are found with the Successive Overrelaxation algorithm, which reveals very efficient for energy minimization in this kind of models.Comment: 16 pages, 6 figure

The Heyday of Teleology and Early Modern Philosophy

Philosoph

Fewer non‐native insects in freshwater than in terrestrial habitats across continents

Aim Biological invasions are a major threat to biodiversity in aquatic and terrestrial habitats. Insects represent an important group of species in freshwater and terrestrial habitats, and they constitute a large proportion of non-native species. However, while many non-native insects are known from terrestrial ecosystems, they appear to be less represented in freshwater habitats. Comparisons between freshwater and terrestrial habitats of invader richness relative to native species richness are scarce, which hinders syntheses of invasion processes. Here, we used data from three regions on different continents to determine whether non-native insects are indeed under-represented in freshwater compared with terrestrial assemblages. Location Europe, North America, New Zealand. Methods We compiled a comprehensive inventory of native and non-native insect species established in freshwater and terrestrial habitats of the three study regions. We then contrasted the richness of non-native and native species among freshwater and terrestrial insects for all insect orders in each region. Using binomial regression, we analysed the proportions of non-native species in freshwater and terrestrial habitats. Marine insect species were excluded from our analysis, and insects in low-salinity brackish water were considered as freshwater insects. Results In most insect orders living in freshwater, non-native species were under-represented, while they were over-represented in a number of terrestrial orders. This pattern occurred in purely aquatic orders and in orders with both freshwater and terrestrial species. Overall, the proportion of non-native species was significantly lower in freshwater than in terrestrial species. Main conclusions Despite the numerical and ecological importance of insects among all non-native species, non-native insect species are surprisingly rare in freshwater habitats. This is consistent across the three investigated regions. We review hypotheses concerning species traits and invasion pathways that are most likely to explain these patterns. Our findings contribute to a growing appreciation of drivers and impacts of biological invasions

Matching microscopic and macroscopic responses in glasses

Primero reproducimos en las computadoras Janus y Janus II un experimento importante que mide la longitud de la coherencia de los hilados de vidrio a través de la reducción de las barreras de energía libre inducidas por el efecto Zeeman. En segundo lugar, determinamos el comportamiento de escala que permite un análisis cuantitativo de un nuevo experimento informado en la Carta complementaria [S. Guchhait y R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. El valor de la longitud de coherencia estimada a través del análisis de las funciones de correlación microscópicas resulta ser cuantitativamente consistente con su medición a través de las funciones de respuesta macroscópica. Además, las susceptibilidades no lineales, recientemente medidas en líquidos formadores de vidrio, se escalan como potencias de la misma longitud microscópica.We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spin glass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly, we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, nonlinear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.• European Research Council. Beca No. NPRGGLASS. Ayuda para Marco Baity Jesi • Unión Europea. Marie Skłodowska- Curie. Beca No. 654971 • Consejo Europeo de Investigación (ERC). Subvención 694925 • University of Syracuse. Beca No. NSF-DMR-305184, para David Yllanes Mosquera • Ministerio de Economía y Competitividad. No. FIS2012-35719-C02, No. FIS2013-42840-P (I+D+i), No. FIS2015-65078-C2, No. FIS2016-76359-P (I+D+i), y No. TEC2016-78358-R • Junta de Extremadura y Fondos FEDER. Contrato parcial GRU10158 • Dipùtación General de Aragón y Fondos Social Europeo. AyudapeerReviewe