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Are there any critical phenomena where the timescale and lengthscale diverge identically with temperature?
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For example, many critical phenomena (phase transitions, etc.) have a diverging lengthscale that goes as
ξ ∼ (T−Tc)α
where Tc is the critical temperature. The characteristic dynamics of this system will then scale as
τ ∼ ξz ∼ (T−Tc)zα
Are there any systems where z=1 , meaning that the static and dynamic divergences scale to the same power α with respect to temperature?
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