Thermodynamics and dynamics of systems with long-range interactions

Systems with long-range interactions have an interaction potential that decays slower than 1/rd at large separation r in d dimensions. Common examples are plasmas, gravitational systems, dipolar ferroelectrics and ferromagnets. Long-range interacting systems are intrinsically non-additive: the sum of energies of macroscopic subsystems is not equal to the energy of the whole system. This leads to many unusual and striking properties, both thermodynamic (e.g., negative microcanonical specific heat, inequivalence of statistical ensembles) and dynamic (e.g., slow relaxation, breaking of ergodicity). After a brief review, I will give an overview of my work on characterizing static and dynamic properties of several analytically tractable examples of long-range interacting systems.