Structural phase transitions with random strains

Abstract

The author presents a physically realizable random field model in the form of dilute crystals undergoing structural phase transitions, with the impurities generating a random strain field. The mode softening that occurs at the transition is anisotropic. The author shows how this anisotropic mode softening reduces the upper critical dimension from 6 to 4. The author performs an in -expansion at three dimensions about the upper critical dimension, from which the author obtains static critical exponents which, to O( in ), are equal to those corresponding to the pure three-dimensional Ising model. The crossover behaviour is described. Elastic long-range forces reduce the upper critical roughening dimension from 5 to 3. The author finds that even at the upper critical roughening dimension of 3, domain wall roughness is not eliminated. This is due to anisotropic shape effects in the domain walls, induced by the anisotropic long-range forces.