This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought.
A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of
both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.
A. Campa is Senior Scientist at the Health and Technology Department of the Istituto Superiore di Sanita, Roma (Italy). He holds a Laurea in Physics (University of Roma "La Sapienza") and a Ph.D. in Physics (The Rockefeller University, New York, USA). His activities are in statistical physics, nonlinear dynamics, radiation physics, and modelling of ionizing radiation effects on biological systems. He worked as a postdoc of the Italian National Institute of the Physics of Matter (INFM) and he is now associated to the Italian National Institute of Nuclear Physics (INFN). T. Dauxois is a CNRS Research Director at the Ecole Normale Superieure de Lyon (France). His scientific activity is in nonlinear physics and statistical physics, with applications to condensed matter and hydrodynamics. He was the Head of Graduate Studies in Physics (M2) at ENS-Lyon (2005-11), Chairman of the Committee for Theoretical Physics in CNRS (2010-12) and is now Director of the Physics Laboratory at ENS de Lyon. D. Fanelli is Associate Professor in the Department of Physics and Astronomy at the University of Florence (Italy). Fanelli's research interests fall in the realm of statistical mechanics and nonlinear physics, with applications to biology and biophysics. He holds a Laurea in Physics (University of Florence) and a Ph.D. In Numerical Analysis and Computer Science (KTH, Stockholm). He worked as a postdoc and researcher at the Karolinska Institute in Stockholm and as permanent staff member (Lecturer in Theoretical Physics) at the University of Manchester. He was also awarded the prestigious "Rientro dei Cervelli" grant. S. Ruffo is a Full Professor in the Department of Physics and Astronomy of the University of Florence (Italy). His scientific activity is in the field of statistical and nonlinear physics. He is an editor of 'Communications in Nonlinear Science and Numerical Simulations'. He has been Weston Visiting Professor at The Weizmann Institute of Science, Department of Physics of Complex Systems (2009-2010) and "Chaire d'Excellence ANR" at the Physics Laboratory of ENS-Lyon (2010-13). He is the Chairman of the C3 Commission (Statistical Physics) of IUPAP.
PART I: STATIC AND EQUILIBRIUM PROPERTIES; PART II: DYNAMICAL PROPERTIES; PART III: APPLICATIONS