A field-theoretical study was made of interacting dislocation loops, and their effect upon the elastic moduli of isotropic 3-dimensional solids. It was found that the shear modulus decreased to a finite limit with increasing density and size of the dislocation loops, and vanished only upon the appearance of open dislocation lines that terminated at the boundaries of the sample. By using the random phase approximation, the correlation between so-called dislocation charges and currents was analyzed and it was shown that interaction between dislocations led to the screening of long-range correlations. Variational and perturbation methods were used to show that fluctuation-induced attraction between segments of dislocation loop led to a shrinking of the radii of gyration of loops as compared with their Gaussian dimensions.

Statistical Physics of Interacting Dislocation Loops and their Effect on the Elastic Moduli of Isotropic Solids. S.Panyukov, Y.Rabin: Physical Review B, 1999, 59[21], 13657-71