Critical phenomena form a central, unifying theme for all members of the SP side of the AMRC. Theoretical approaches include the renormalization group, conformal field theory, Coulomb gas methods and stochastic Loewner evolution. Applications include at a fundamental level as well as to experimentally realisable, disordered and glassy systems and technologically important phenomena such as high-temperature superconductors, colossal magnetoresistance and the anomalous Hall effect. In collaboration with Holovatch, Palchykov (Lviv) and Folk (Linz), von Ferber investigated critical phenomena on scale free networks, and his team was the first to include coupled order parameters for such systems. With Ruiz Lorenzo (Extremadura), Kenna resolved a 30-year old controversy regarding scaling impurities by a combination of new theoretical insights and solid numerics. With Foster (Cergy) and Hsu (Mainz), von Ferber and Kenna developed Fisher renormalization at the upper critical dimension, of importance for realistic, impure condensed-matter systems under constraint. With Berche (Lorraine), Kenna developed hyperscaling and universal finite-size scaling above the upper critical dimension and transformed our fundamental understanding of finite-systems with free boundaries there. Izmailian studied universality of ratios among scaling amplitudes, and finite-size effects in spin models, dimer models and non-local phenomena, magnetic films, conformal field theory, and exactly solvable models. Weigel also studied universal amplitudes deduced from conformal field theory in 2D and 3D. Studies of geometrical critical phenomena with Stevenson (Cambridge), exploited their relation to Stochastic Loewner Evolution. Using novel techniques developed by Weigel for this purpose and large-scale simulations on HPC facilities, allowed to understand the scaling of defect energies in 2d XY spin glasses with Gingras (Waterloo), and the physics of the infinite-component vector spin glass on hypercubic lattices. With M.A. Moore (FRS) from Manchester, Weigel presented a comprehensive analysis of the physics of the one-dimensional infinite-component spin glass with long-range interactions. His study of packing of non-spherical bodies on periodic lattices is relevant to a wide range of fields including structural glasses, granular material and plastic molecules. Platini’s works on the national French project on open quantum systems led to an exact description of stationary states of open quantum systems. This work, successfully applied to transport phenomena, has been selected (by IOP's editors) for its novelty, significance and potential impact on future research. Over the last years, Platini's research on the characterization of non-equilibrium steady states led to a measure of the violation of 'detailed balance' and exact results for some of the favourite models of the community.

With Blavatska and Holovatch (Lviv) von Ferber investigates the behaviour of multi-component star polymers in porous environments by field theoretic methods their scaling properties and showed how these manifest in observable behaviour. They further showed how the disordered environment impacts on the shape of corresponding polymers. von Ferber collaborates with Bishop and Monteith (New York) investigating the shapes of two dimensional macromolecules. Over the last couple of years, Platini expanded his research works towards bio-physics. In collaboration with researchers in at Virginia Tech and Virginia Bio Informatics Institute, he developed new analytical approaches to stochastic modelling of gene expression.

In a series of pioneering works at the interface of physics and high-performance computing, Weigel could show how graphics processing units (GPUs) can be used as general computational devices for simulations of lattice-spin systems, leading to up to 1000-fold speed-ups compared to CPUs. Weigel’s research also includes extensions of the simulational toolbox, including multicanonical simulations for spin models, or a general demonstration of how cross-correlations in data from a wide range of experimental and simulational studies have previously been neglected but, if taken into account properly, can lead to improved precision estimates.

Von Ferber leads a collaboration with Berche (Nancy), and Holovatch (Lviv) on public transit networks (PTNs). Their research identified common features such as scaling and small-world phenomena and discovered a particular “harness effect” – a concept since been taken up in the field. They showed that there are strong variations in PTNs’ resilience to attack or failure and criteria they developed are planned to be applied in collaboration with Transport Authorities (contacts with Centro, the West Midlands Authority are currently being made). A number of papers by Kenna and Berche on the relationship between quality and quantity in research (critical mass, etc.), attracted considerable attention in the media and amongst policy makers (Case Study 2). He also pioneered an application of network theory to the humanities, through the first ever quantitative study of comparative mythology. This Leverhulme-supported work also gained enormous interest in the media and public at large. (Both papers were featured as “Best of” EPL.) Weigel completed work on goal distributions in ball sports. In these studies the authors were able to explain the observed distributions from an elegant and exactly solvable microscopic model. These works have been met with an extraordinary general interest inside and outside of the scientific community.