Mermin–Wagner theorem
In quantum field theory and statistical mechanics, the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2. Intuitively, this theorem implies that long-range fluctuations can be created with little energy cost, and since they increase the entropy, they are favored.