Statistical Field Theory

At criticality, the correlation length of a statistical model diverges and the system loses a characteristic length scale. This scale invariance at the critical point makes it natural to model a wide range of systems, classical or quantum, in terms of statistical field theory. This allows the use of field theoretical methods with the understanding that critical points correspond to renormalization group fixed points of a given model in theory space. This picture sheds light into the emerging universal properties at critical points in systems undergoing phase transitions.