Linked-cluster Expansions for Lattice Spin Models

Similar to various series expansions that are used to approximate mathematical func- tions, the linked-cluster expansion is an approximation method that allows us to approach the actual values of a very large physical system’s different physical quan- tities by systematically studying smaller systems embedded in this larger system. The main concept in linked-cluster expansion, weight, represents the additional con- tribution to a certain physical quantity by increasing the system size by one unit. These weights are used to eventually build up the result on a larger system. In our case, we focus on the partition function, a quantity that can be used to calculate several essential thermodynamic aspects of the system such as average energy, spe- cific heat, magnetic susceptibility, etc. We study these weights for the Ising and Potts models on a one dimensional lattice and Bethe lattice, with and without an external magnetic field. Previous studies have shown that in the one dimensional Ising model, adding more than two lattice sites to the system does not create any ad- ditional contribution to the partition function (i.e. their weights are all zero), giving us the result for an infinitely large system with just two lattice sites, a remarkable simplification. In our study, we prove that this property holds not only for the Ising model, but also its generalization, the Potts model, and show that it is a result of a spin flip symmetry inherent in the system. In order to test this, we break this symmetry using an externally applied magnetic field and show that in this case, for magnetic dipole energies comparable with the exchange energy between neighboring spins, this special property vanishes

Linked cluster expansion on trees

The linked cluster expansion has been shown to be highly efficient in calculating equilibrium and nonequilibrium properties of a variety of 1D and 2D classical and quantum lattice models. In this article, we extend the linked cluster method to the Cayley tree and its boundaryless cousin the Bethe lattice. We aim to (a) develop the linked cluster expansion for these lattices, a novel application, and (b) to further understand the surprising convergence efficiency of the linked cluster method, as well as its limitations. We obtain several key results. First, we show that for nearest-neighbor Hamiltonians of a specific form, all finite treelike clusters can be mapped to one dimensional finite chains. We then show that the qualitative distinction between the Cayley tree and Bethe lattice appears due to differing lattice constants that is a result of the Bethe lattice being boundaryless. We use these results to obtain the explicit closed-form formula for the zero-field susceptibility for the entire disordered phase up to the critical point for Bethe lattices of arbitrary degree; remarkably, only 1D chainlike clusters contribute. We also obtain the exact zero field partition function for the Ising model on both trees with only the two smallest clusters, similar to the 1D chain. Finally, these results achieve a direct comparison between an infinite lattice with a nonnegligible boundary and one without any boundary, allowing us to show that the linked cluster expansion eliminates boundary terms at each order of the expansion, answering the question about its surprising convergence efficiency. We conclude with some ramifications of these results, and possible generalizations and applications.Comment: 10 pages, 8 figure

Beam Test Results of the RADiCAL -- a Radiation Hard Innovative EM Calorimeter

High performance calorimetry conducted at future hadron colliders, such as the FCC-hh, poses a significant challenge for applying current detector technologies due to unprecedented beam luminosities and radiation fields. Solutions include developing scintillators that are capable of separating events at the sub-fifty picosecond level while also maintaining performance after extreme and constant neutron and ionizing radiation exposure. The RADiCAL is an approach that incorporates radiation tolerant materials in a sampling 'shashlik' style calorimeter configuration, using quartz capillaries filled with organic liquid or polymer-based wavelength shifters embedded in layers of tungsten plates and LYSO crystals. This novel design intends to address the Priority Research Directions (PRD) for calorimetry listed in the DOE Basic Research Needs (BRN) workshop for HEP Instrumentation. Here we report preliminary results from an experimental run at the Fermilab Test Beam Facility in June 2022. These tests demonstrate that the RADiCAL concept is capable of < 50 ps timing resolution.Comment: 5 pages, 10 figures, SCINT22 conferenc

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

Beyond biogeographic patterns: Processes shaping the microbial landscape in soils and sediments along the Yangtze River

Abstract Deciphering biogeographic patterns of microorganisms is important for evaluating the maintenance of microbial diversity with respect to the ecosystem functions they drives. However, ecological processes shaping distribution patterns of microorganisms across large spatial‐scale watersheds remain largely unknown. Using Illumina sequencing and multiple statistical methods, we characterized distribution patterns and maintenance diversity of microorganisms (i.e., archaea, bacteria, and fungi) in soils and sediments along the Yangtze River. Distinct microbial distribution patterns were found between soils and sediments, and microbial community similarity significantly decreased with increasing geographical distance. Physicochemical properties showed a larger effect on microbial community composition than geospatial and climatic factors. Archaea and fungi displayed stronger species replacements and weaker environmental constraints in soils than that in sediments, but opposite for bacteria. Archaea, bacteria, and fungi in soils showed broader environmental breadths and stronger phylogenetic signals compared to those in sediments, suggesting stronger environmental adaptation. Stochasticity dominated community assemblies of archaea and fungi in soils and sediments, whereas determinism dominated bacterial community assembly. Our results have therefore highlighted distinct microbial distribution patterns and diversity maintenance mechanisms between soils and sediments, and emphasized important roles of species replacement, environmental adaptability, and ecological assembly processes on microbial landscape. Our findings are helpful in predicting loss of microbial diversity in the Yangtze River Basin, and might assist the establishment of environmental policies for protecting fragile watersheds

Spatial difference in phoD-harboring bacterial landscape between soils and sediments along the Yangtze River

Deciphering biogeographical patterns of alkaline phosphatase (phoD)-harboring bacteria is essential to understand organic phosphorus mineralization. However, it is poorly understood about distribution pattern and diversity maintenance mechanisms of phoD-harboring bacteria (PHB) in watershed ecosystems. Here, we estimated ecological processes shaping landscape of PHB in soils and sediments along the Yangtze River. The PHB community similarity decayed against higher geographical distance at taxonomic and phylogenetic levels, and larger compositional variation in PHB community were found in sediments only. The PHB displayed higher α-diversities, broader environmental breadths, higher community stability, and stronger species replacement in soils. Conversely, PHB showed stronger phylogenetic signals in sediments. Stochastic and differentiating processes dominated community assemblies of PHB in both soils and sediments. Electrical conductivity displayed decisive roles in shaping PHB diversity for soils and sediments at taxonomic and phylogenetic levels. Our results emphasized differences in distribution patterns of PHB between soils and sediments, and highlighted ecological processes shaping landscapes of PHB in soils and sediments along the Yangtze River. The phosphorus cycling-related findings might be helpful to estimate ecological potential of a watershed ecosystem and could provide new insights for ecological protection policy for the Yangtze River