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Quantum chromodynamics
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===Additional remarks: duality=== As mentioned, ''asymptotic freedom'' means that at large energy – this corresponds also to ''short distances'' – there is practically no interaction between the particles. This is in contrast – more precisely one would say ''[[Kramers–Wannier duality|dual]]''– to what one is used to, since usually one connects the absence of interactions with ''large'' distances. However, as already mentioned in the original paper of Franz Wegner,<ref>{{cite journal |last=Wegner |first=F. |year=1971 |title=Duality in Generalized Ising Models and Phase Transitions without Local Order Parameter |journal=J. Math. Phys. |volume=12 |issue=10 |pages=2259–2272 |bibcode=1971JMP....12.2259W |doi=10.1063/1.1665530}} Reprinted in {{cite book |title=Lattice Gauge Theories and Monte Carlo Simulations |publisher=World Scientific |year=1983 |isbn=9971950707 |editor-last=Rebbi |editor-first=Claudio |location=Singapore |pages=60–73}} Abstract: [http://www.tphys.uni-heidelberg.de/~wegner/Abstracts.html#12] {{webarchive|url=https://web.archive.org/web/20110504173247/http://www.tphys.uni-heidelberg.de/~wegner/Abstracts.html|date=2011-05-04}}</ref> a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the ''original model'', e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!) ''dual model'', namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article.<ref>Perhaps one can guess that in the "original" model mainly the quarks would fluctuate, whereas in the present one, the "dual" model, mainly the gluons do.</ref>
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