MerminWagnerHohenberg
The Mermin-Wagner-Hohenberg theorem is a fundamental result in the theory of phase transitions and critical phenomena in two-dimensional systems. It was independently proven by Norman Mermin and John Michael Kosterlitz in 1966, and later extended by Michael Hohenberg in 1967. The theorem states that continuous symmetry breaking cannot occur in two-dimensional systems at finite temperatures, except in the case of the XY model with a vortex-antivortex pair unbinding transition. This means that systems with continuous symmetries, such as the two-dimensional Ising model, cannot exhibit a true phase transition at any finite temperature. Instead, they exhibit a Kosterlitz-Thouless transition, where topological defects (vortices) play a crucial role.
The theorem is based on the concept of topological defects and the behavior of the correlation functions
The Mermin-Wagner-Hohenberg theorem has significant implications for our understanding of phase transitions and critical phenomena. It