Coexistence of Two Length Scales in X-Ray and Neutron Critical Scattering: A Theoretical Interpretation

Abstract

The theory of critical phenomena in the presence of quenched disorder is applied to x-ray and neutron experiments which suggest two different length scales for critical fluctuations. Long-range random strains associated with defects generated near the sample surface can induce crossover to a ``disordered'' fixed point with different critical exponents, while the bulk retains the ordinary critical behavior. For Ho and Tb, it is proposed that the dominant defects are dislocation dipoles, resulting in a critical exponent for the second correlation length ${\ensuremath{\nu}}_{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, in reasonable agreement with experiments.