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Abstract
A variety of two- and three-dimensional random frustrated systems with continuous and discrete symmetries are studied within the Migdal-Kadanoff renormalization-group scheme. The continuous-symmetry {ital XY} models are approximated by discretized clock models with a large number of clock states. In agreement with earlier studies of the random gauge {ital XY} model using a {ital T}=0 scaling approach, a nonzero transition temperature is observed in three-dimensional {ital XY} models with O(2) local gauge invariance. Our analysis points to the possible importance of local gauge invariance in determining the lower critical dimensionality of frustrated systems.
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