The Mermin-Wagner Theorem states that a continuous symmetry cannot be spontaneously broken at nonzero temperature in a system with sufficiently short-range interactions confined to one or two spatial dimensions, so the long-range magnetic order familiar from three-dimensional magnets cannot occur there. Named for N. David Mermin and Herbert Wagner, it is a foundational no-go result of statistical mechanics constraining what kinds of order low-dimensional systems can sustain.
Facts
StatementContinuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions of two or fewer. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Mermin-Wagner theorem, Wikipedia
Introduction section, opening sentence
continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d less than or equal to 2
Introduction section, history sentence
The absence of spontaneous symmetry breaking in d less than or equal to 2 dimensional infinite systems was rigorously proved by David Mermin and Herbert Wagner (1966)
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