advanced_notions:symmetry_breaking:mermin-wagner_theorem
| Next revision | Previous revision Next revision Both sides next revision | ||
|
advanced_notions:symmetry_breaking:mermin-wagner_theorem [2017/09/29 07:53] jakobadmin created |
advanced_notions:symmetry_breaking:mermin-wagner_theorem [2017/10/27 13:07] jakobadmin ↷ Page moved from symmetry_breaking:mermin-wagner_theorem to advanced_notions:symmetry_breaking:mermin-wagner_theorem |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| + | <blockquote>A theorem due to Mermin and Wagner states that a continuous symmetry can only be spontaneously broken in a dimension larger than two. For a discrete symmetry this lower critical dimensionality is one. This is, in fact, well known since in quantum mechanics with finitely many degrees of freedom (corresponding to one-dimensional field theory) tunneling between degenerate classical minima allows for a unique symmetric ground state. [...] The Mermin-Wagner theorem has been restated by Coleman in the framework of field theory. <cite>page 525 in Quantum Field Theory by Claude Itzykson, Jean-Bernard Zuber </cite> </blockquote> | ||
| <tabbox Layman> | <tabbox Layman> | ||
| Line 19: | Line 20: | ||
| Take note that the Mermin-Wagner theorem is not so universal as it is presented most of the time: | Take note that the Mermin-Wagner theorem is not so universal as it is presented most of the time: | ||
| - | <blockquote>12In two dimensions, crystals provide another loophole in a well-known result, known as the Mermin–Wagner theorem. Hohenberg, | + | <blockquote>In two dimensions, crystals provide another loophole in a well-known result, known as the Mermin–Wagner theorem. Hohenberg, |
| Mermin, and Wagner, in a series of papers, proved in the 1960s that two-dimensional systems with a continuous symmetry | Mermin, and Wagner, in a series of papers, proved in the 1960s that two-dimensional systems with a continuous symmetry | ||
| cannot have a broken symmetry at finite temperature. At least, that is the English phrase everyone quotes when they discuss | cannot have a broken symmetry at finite temperature. At least, that is the English phrase everyone quotes when they discuss | ||
advanced_notions/symmetry_breaking/mermin-wagner_theorem.txt · Last modified: 2021/03/18 12:36 by orbital
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
