Statistical Field theory

An enormous progress has been recently achieved in the area of quantum field theory by using ideas, techniques and inspirations coming from Statistical Physics. This is particularly true in the subject of low dimensional systems, where the combination of methods as exact scattering matrix, spectral series, finite-size effects, Bethe Ansatz and so on, has enable us to reach the exact solution of long-standing problems. Among those, the famous problem of the Ising model in a magnetic field, the universal properties of the self-avoiding walks, the exact computation of the geometrical quantities of the percolation, systems with boundaries etc.
The advent of Conformal Field Theory has opened up an exact approach to the critical properties of low-dimensional systems and since then, the field has grown explosively in several directions, including the statistical mechanics of phase transitions and growth phenomena, the modern formulation of strongly interacting systems or topological quantum computation

In the same period, one has also witnessed a parallel development in many fascinating subjects of mathematics, drawing researchers from the communities of infinite dimensional Lie algebras, algebraic geometry, integrable systems, random matrices and probability.