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--- advanced_notions:symmetry_breaking:mermin-wagner_theorem [2017/09/29 07:54]
jakobadmin [Researcher]
+++ 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
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 <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>