Mermin-Wagner theorem

This is a specific case of what is called the Mermin-Wagner theorem in spin systems.

This is the Mermin-Wagner theorem: there is no spontaneous breaking of a continuous symmetry in two dimensions.

As a postdoc at Cornell University, he and David Mermin (and independently of Pierre Hohenberg) proved a "no-go theorem", otherwise known as the Mermin-Wagner theorem.

Nathaniel David Mermin is a solid-state physicist at Cornell University best known for the eponymous Mermin-Wagner theorem, his application of the term "Boojum" to superfluidity, and for the quote "Shut up and calculate!"

In quantum field theory and statistical mechanics, the Mermin-Wagner theorem (also known as Mermin-Wagner-Hohenberg theorem or Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d 2.

Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations will grow logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size.