Janus II: a new generation application-driven computer for spin-system simulations

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures, which can be implemented with available electronics technologies, may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.Comment: 28 pages, 6 figure

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

Massively parallel simulations for disordered systems

Simulations of systems with quenched disorder are extremely demanding, suffering from the combined effect of slow relaxation and the need of performing the disorder average. As a consequence, new algorithms, improved implementations, and alternative and even purpose-built hardware are often instrumental for conducting meaningful studies of such systems. The ensuing demands regarding hardware availability and code complexity are substantial and sometimes prohibitive. We demonstrate how with a moderate coding effort leaving the overall structure of the simulation code unaltered as compared to a CPU implementation, very significant speed-ups can be achieved from a parallel code on GPU by mainly exploiting the trivial parallelism of the disorder samples and the near-trivial parallelism of the parallel tempering replicas. A combination of this massively parallel implementation with a careful choice of the temperature protocol for parallel tempering as well as efficient cluster updates allows us to equilibrate comparatively large systems with moderate computational resources.Comment: accepted for publication in EPJB, Topical issue - Recent advances in the theory of disordered system

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

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, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.Comment: 6 pages, 4 figure

The Mpemba effect in spin glasses is a persistent memory effect

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a non-equilibrium process, governed by the coherence length \xi of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and \xi that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing new avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.Comment: Version accepted for publication in PNAS. 6 pages, 7 figure

The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.Comment: 42 pages, 19 figures. Minor changes and added figure (results unchanged

Critical parameters of the three-dimensional Ising spin glass

We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, \nu = 2.562(42) for the thermal exponent, \eta = -0.3900(36) for the anomalous dimension and \omega = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield \alpha = -5.69(13), \beta = 0.782(10) and \gamma = 6.13(11). We also compute several universal quantities at Tc.Comment: 9 pages, 5 figure

Aging rate of spin glasses from simulations matches experiments

Experiments on spin glasses can now make precise measurements of the exponent $z(T)$ governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for $z(T)$ have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent $z(T, t_w)$, which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the $T = T_c$ and $T = 0$ fixed points.Comment: Version accepted for publication in PRL. 12 pages, 9 figure

Temperature chaos is present in off-equilibrium spin-glass dynamics

Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ¿. Indeed, an emerging length-scale ¿* rules the crossover from weak (at ¿ « ¿*) to strong chaos (¿ » ¿*). Extrapolations of ¿* to relevant experimental conditions are provided. © 2021, The Author(s)