Order operator

In quantum field theory, an order operator or an order field is a quantum field version of Landau's order parameter whose expectation value characterizes phase transitions. There exists a dual version of it, the disorder operator or disorder field, whose expectation value characterizes a phase transition by indicating the prolific presence of defect or vortex lines in an ordered phase.

The disorder operator is an operator that creates a discontinuity of the ordinary order operators or a monodromy for their values. For example, a 't Hooft operator is a disorder operator. So is the Jordan-Wigner transformation. The concept of a disorder observable was first introduced in the context of 2D Ising spin lattices, where a phase transition between spin-aligned (magnetized) and disordered phases happens at some temperature.