The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.

This book represents Volume II of the Proceedings of the UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science, hosted by the National Astronomical Observatory of Japan, Tokyo, 18 - 22 June, 2007. It covers two programme topics explored in this and past workshops of this nature: (i) non-extensive statistical mechanics as applicable to astrophysics, addressing q-distribution, fractional reaction and diffusion, and the reaction coefficient, as well as the Mittag-Leffler function and (ii) the TRIPOD concept, developed for astronomical telescope facilities. The companion publication, Volume I of the proceedings of this workshop, is a special issue in the journal Earth, Moon, and Planets, Volume 104, Numbers 1-4, April 2009.

The proceedings of this workshop contains 5 important papers by S A Edwards on the Edwards Model and includes discussions on recent theoretical developments in polymer physics.A few decades ago, polymers were not considered part of conventional physics. However, the scenario changed drastically in the sixties and seventies with the introduction of path integral methods, fields theory in the n → limits, and renormalization group approach. A vital step in this progress is the path integral Hamiltonian that S F Edwards proposed in 1965-66 to study a single chain. This model now called the Edwards model, is considered to be the minimal model for polymers, and it has been phenomenal in unraveling the universal properties of polymers, be it a single chain or many, equilibrium or dynamics. It has now crossed the boundary of polymers and is finding applications through appropriate generalizations in many other problems.

Deciphering the script for the Big Bang has now become a joint effort of particle physicists and cosmologists. The origin and first moments of the early Universe were determined by the same fundamental processes which are studied in terrestrial accelerators and whose traces from the early Universe can be seen in astrophysical observations. It is now almost universally accepted that most of the debris left over from the Big Bang is likely to be in the form of particle dark matter. Identifying its nature and measuring its abundance in the Universe have become major goals of theorists and experimentalists alike. This volume reviews the progress made at the frontiers of research in these rapidly expanding fields. A broad range of topics, from inflation to primordial black holes to physics at the Planck era, and to dark matter and neutrinos — both reviews and reports on the most recent advances — is presented by leaders in the field.

Contents:Critical Phenomena, Field Theory and Renormalisation Group (T-M Yan & S C-C Lin)Field Theories of Surfaces and Interfaces (S C-C Lin)Spiral Self-Avoiding Walks (K Y Lin)Critical Phenomena on Fractal Lattices (Doochul Kim)Percolation and Phase Transitions: Towards a Unified Theory of Phase Transitions (C-K Hu)Real Space Approach to Disordered Systems (S-Y Wu)Three Routes to Chaos: Period Doubling, Intermittency and Quasiperiodicity (B Hu)Ordering Kinetics in Phase Transitions (K Kawasaki)A Design of Analog Circuit for Studies of Transitions to Chaos in a RF-Driven Josephson Junction (J C Huang et al)Potts Model and Graph Theory (F Y Wu)Number and Size of Convex Polygons on the Square Lattice (K Y Lin)Exactly Solvable Models in Statistical Mechanics and Automorphisms of Algebraic Varieties (J-M Maillard)The Application of the Transfer Matrix Method to the Phase Transition of Ising Model (T Oguchi et al)Coherent-Anomaly Method in Critical Phenomena (M Katori & M Suzuki)Monte Carlo Study of Percolation Transitions and Phase Transitions in Interacting Systems (C-K Hu & K-S Mak)Anisotropic Surface Tension and Equilibrium Crystal Shapes (R K P Zia)The Structure Making and Breaking Effects of Ion Solvation in Water (J-L Lin & C-Y Mou)Ordering Processes in Two-Dimensional Quantum Spin Systems (S=1/2) (S Miyashita)Phase Transitions in Arrays of Josephson Junctions (M Y Choi) Readership: Theoretical physicists and condensed matter physicists.