From Landau's order parameter to modern disorder fields

Abstract

Landau's work was crucial for the development of the modern theory of phase transitions. He showed that such transitions can be classified by an order parameter, which in the low-temperature phase becomes nonzero. Together with Ginzburg he made this order parameter a spacetime-dependent order field and introduced a local energy functional whose extrema yield field equations and whose fluctuations determine the universal critical behavior of second-oder transitions. In the same spirit, but from a dual point of view, I have developed in the last twenty years a disorder field theory that describes phase transitions via the statistical mechanics of grand-canonical ensembles of vortex lines in superfluids and superconductors, or of defect lines in crystals. The Feynman diagrams of the disorder fields are pictures of the vortex or defect lines. A nonzero ground state expectation value of the disorder field at high temperature signalizes the proliferation of line like excitations in the ordered phase. It was this description of the superconductor that led in 1982 to a first understanding of the order of the superconducting phase transition. Recent experimental progress in the critical regime of high-Tc superconductors will be able to verify the predicted tricritical point of the Ginzburg parameter κ≈0.8/√2 where the second-order transition becomes first-order. © 2010 American Institute of Physics.