# Neutron scattering for a critical magnetic-ordering system : what about critical opalescence?

Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model.

We know that the liquid-gas transition is characterized by a phenomenon called critical opalescence that occurs at the critical point and which in short happens because the system becomes correlated at all length scales and thus scatters all frequency of the incident light, thus making the liquid-gas look opaque.

Q : What is the analogous phenomenon of critical opalescence in a spin system ? Say one takes a material that may be described by a 3D Ising model and does neutron scattering with a broad range of neutron energy : At the critical magnetic ordering temperature, will he see critical opalescence of the neutrons, i.e a diffuse scattering of the neutrons at all wave-length at the critical temperature ?

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I'm not sure about neutron scattering, but the correlation length of the spin states increases until it reaches the system size. As you cross the critical point, spontaneous magnetization can or cannot occur, depending on whether $T<T_c$ or $T>T_c$, where $T$ is the temperature and $T_c$ is the Curie temperature. – Douglas B. Staple Apr 19 '13 at 16:44

After thinking a bit : We know that at the critical temperature the correlation diverges and this means that the spin-spin correlation function obeys an algebraic decay (power law) at the critical temperature ($T_c$), i.e. that correlations are long-ranged (in opposition to short-ranged with and exponential decay). A diffuse neutron scattering map basically constitute the Fourier transform of the spin-spin correlation function an appear as an intensity map of the scattered neutrons in reciprocal space. If one has long-ranged correlations, the magnetic features are expected to become very sharp at the critical temperature. This stems from the fact that if one has a broad decaying correlation function in real-space, the corresponding feature in Fourier space will be sharp. The appearance of sharp features in reciprocal space of the neutron scattering maps is thus analogous to the phenomena of critical opalescence for light.