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Surprising as it may seem, applications of statistical methods to physics were inspired by the social sciences, which in turn are linked to the humanities. So perhaps it is not as unlikely as it might first appear for a group of statistical physicists and humanists to come together to investigate one of the subjects of Thomas Jefferson's poetic interests from a scientific point of view. And that is the nature of this article: a collaborative interdisciplinary analysis of the works of a figure Jefferson described as a ''rude bard of the North'' and ''the greatest Poet that has ever existed.'' In 2012, a subset of this team embraced an increase in interdisciplinary methods to apply the new science of complex networks to longstanding questions in comparative mythology. Investigations of network structures embedded in epic narratives allowed universal properties to be identified and ancient texts to be compared to each other. The approach inspired new challenges in mathematics, physics and even processes in industry, thereby illustrating how collaborations of this nature can be mutually beneficial and can capture the attention of a public, often ill-served by academic communication and dissemination. This article derives from these works, and from our consistent objective to help bridge the perceived gap between the natural sciences and the humanities. First we discuss the history of relationships between the two. Then we discuss the origins of the poems of Ossian and Jefferson's interests. We follow with our statistical approach in the next section. In the final section, we explore ideas for future research on these themes and discuss the potential of collaborative pursuits of human curiosity to overcome the two cultures dichotomy and embrace a scientific- and humanities-literate information age., Contriution to book chapter

Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts such as universality, finite-size scaling and hyperscaling, until recently believed not to be applicable above the upper critical dimension. Significant theoretical progress has been made resolving these issues, and tested in numerous simulational studies of spin models. This progress rests upon superlinearity of correlation length, a notion that for a long time encountered resistance but is now broadly accepted. Percolation theory brings added complications such as proliferation of interpenetrating clusters in apparent conflict with suggestions coming from random-graph asymptotics and a dearth of reliable simulational guidance. Here we report on recent theoretical progress in percolation theory in the renormalization group framework in high dimensions that accommodates superlinear correlation and renders most of the above concepts mutually compatible under different boundary conditions. Results from numerical simulations for free and periodic boundary conditions which differentiate between previously competing theories are also presented. Although still fragmentary, these Monte Carlo results support the new framework which restores the renormalization group and foundational concepts on which it rests.

We derive exact finite-size corrections for the free energy $F$ of the Ising model on the ${\cal M} \times 2 {\cal N}$ square lattice with Brascamp-Kunz boundary conditions. We calculate ratios $r_p(\rho)$ of $p$th coefficients of F for the infinitely long cylinder (${\cal M} \to \infty$) and the infinitely long Brascamp-Kunz strip (${\cal N} \to \infty$) at varying values of the aspect ratio $\rho={(\cal M}+1) / 2{\cal N}$. Like previous studies have shown for the two-dimensional dimer model, the limiting values $p \to \infty$ of $r_p(\rho)$ exhibit abrupt anomalous behaviour at certain values of $\rho$. These critical values of $\rho$ and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models., Comment: Supplementary material included with the paper

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems., Comment: 29 pages, 11 figures

Tracing the evolution of specific topics is a subject area which belongs to the general problem of mapping the structure of scientific knowledge. Often bibliometric data bases are used to study the history of scientific topic evolution from its appearance to its extinction or merger with other topics. In this chapter the authors present an analysis of the academic response to the disaster that occurred in 1986 in Chornobyl (Chernobyl), Ukraine, considered as one of the most devastating nuclear power plant accidents in history. Using a bibliographic database the distributions of Chornobyl-related papers in different scientific fields are analysed, as are their growth rates and properties of co-authorship networks. Elements of descriptive statistics and tools of complex-network theory are used to highlight interdisciplinary as well as international effects. In particular, tools of complex-network science enable information visualization complemented by further quantitative analysis. A further goal of the chapter is to provide a simple pedagogical introduction to the application of complex-network analysis for visual data representation and interdisciplinary communication., Submitted to become a chapter of the book "Information Visualization Techniques in the Social Sciences and Humanities"

By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing second-order criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed., Comment: Review prepared for the book "Order, Disorder, and Criticality. Vol. III", ed. by Yu. Holovatch and based on the Ising Lectures in Lviv. 48 pages, 1 figure

We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by conformal field theory having central charge $c=1$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $\lambda=1$, while for even $\mathcal{N}$ it is infinite ($\lambda=\infty$). In the former case, therefore, the finite-size specific-heat pseudocritical point is size dependent, while in the latter case, it coincides with the critical point of the thermodynamic limit., Comment: 15 pages, 4 figures

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the quality of statistics and operational research groups and the quantity researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 $\pm$ 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is about twice this value.

Using the results of the UK's research assessment exercise, we show that the size or mass of research groups, rather than individual caliber or prestige of the institution, is the dominant factor which drives the quality of research teams. There are two critical masses in research: a lower one, below which teams are vulnerable and an upper one, above which average dependency of research quality on team size reduces. This leveling off refutes arguments which advocate ever increasing concentration of research support into a few large institutions. We also show that to increase research quality, policies which nourish two-way communication links between researchers are paramount., Comment: 17 pages, 8 figures, each with 3 panels

In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an attempt to fully understand the nature of its transition, which is of the Berezinskii-Kosterlitz-Thouless type. These met with only limited success until it was realized that subtle effects (logarithmic corrections) that modify leading behaviour must be taken into account. This realization prompted renewed activity in the field and significant progress has been made. This paper contains a review of the importance of such subtleties, the role played by vortices and of recent and current research in this area. Directions for desirable future research endeavours are outlined., 5 pages, 1 figure. Short review prepared for the Annals of the Marie Curie Fellowships

We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new way to measure their strengths in the form of latent heat and critical exponents. Application to a number of models demonstrates the efficacy of the technique., Comment: 5 pages, LaTeX, 3 postscript figures, to appear in: Computer Simulation Studies in Condensed Matter Physics XIV, ed. by D.P. Landau, S.P Lewis, and H.-B. Sch"uttler