Editing Critical phenomena (section)

==Critical dynamics==
Critical phenomena may also appear for ''dynamic'' quantities, not only for ''static'' ones. In fact, the divergence of the characteristic ''time'' <math>\tau </math> of a system is directly related to the divergence of the thermal ''correlation length'' <math>\xi </math> by the introduction of a dynamical exponent ''z'' and the relation <math>\tau =\xi^{\,z}</math>&nbsp;.<ref>P. C. Hohenberg und B. I. Halperin, ''Theory of dynamic critical phenomena'' , Rev. Mod. Phys. 49 (1977) 435.</ref> The voluminous ''static universality class'' of a system splits into different, less voluminous ''dynamic universality classes'' with different values of ''z''
but a common static critical behaviour, and by approaching the critical point one may observe all kinds of slowing-down phenomena. The divergence of relaxation time <math>\tau</math> at criticality leads to singularities in various collective transport quantities, e.g., the interdiffusivity, [[Viscosity|shear viscosity]] <math>\eta\sim \xi^{x_\eta}</math>,<ref>{{Cite journal|last1=Roy|first1=Sutapa|last2=Dietrich|first2=S.|last3=Höfling|first3=Felix|date=2016-10-05|title=Structure and dynamics of binary liquid mixtures near their continuous demixing transitions|url=https://aip.scitation.org/doi/full/10.1063/1.4963771|journal=The Journal of Chemical Physics|volume=145|issue=13|pages=134505|doi=10.1063/1.4963771|pmid=27782419|arxiv=1606.05595|bibcode=2016JChPh.145m4505R|s2cid=37016085|issn=0021-9606}}</ref> and bulk viscosity <math>\zeta \sim \xi^{x_\zeta}</math>. The dynamic critical exponents follow certain scaling relations, viz., <math>z=d+x_\eta</math>, where d is the space dimension. There is only one independent dynamic critical exponent. Values of these exponents are dictated by several universality classes. According to the Hohenberg−Halperin nomenclature,<ref>{{Cite journal|last1=Hohenberg|first1=P. C.|last2=Halperin|first2=B. I.|date=1977-07-01|title=Theory of dynamic critical phenomena|journal=Reviews of Modern Physics|volume=49|issue=3|pages=435–479|doi=10.1103/RevModPhys.49.435|bibcode=1977RvMP...49..435H|s2cid=122636335 }}</ref> for the model H<ref>{{Cite journal|last1=Folk|first1=R|last2=Moser|first2=G|date=2006-05-31|title=Critical dynamics: a field-theoretical approach|journal=Journal of Physics A: Mathematical and General|volume=39|issue=24|pages=R207–R313|doi=10.1088/0305-4470/39/24/r01|issn=0305-4470}}</ref> universality class (fluids) <math>x_\eta \simeq 0.068, z \simeq 3.068</math>.