We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using x-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross section, as a function of the momentum transfer and the scattering angle. Experimental verification using x rays and binary alloys appears well within the existing techniques, while feasibility for neutron scattering requires further study. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

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• Critical phenomena
• Magnetic phase transitions
• Second order phase transitions
• Magnetic systems
• Multi-principal element alloys
• Conformal symmetry
• Grazing-incidence small-angle x-ray scattering
• Small angle neutron scattering