Long-range criticality and the puzzle of crossover to short range

Slava Rychkov (IHES and ENS, Paris)

The classic problem of long-range criticality in lattice models involves statistical mechanics of Ising spins
whose interactions decays as a power law of the distance, as opposed to be nearest neighbor. In 2 and 3 spatial dimensions, this system is known to have a thermodynamic second-order phase transition with critical exponents depending continuously on the power-law exponent in some range, at whose upper end the system transitions to the short-range universality class. The nature of this transition is puzzling from various aspects, and has been a subject of some controversy. We will describe what we believe is a lasting solution to this problem.