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Renormalization-group analysis is employed to investigate the critical behavior of coupled XY models. Recursion relations for small vortex fugacities and Migdal recursion relations in the strong-coupling limit are used to obtain the phase diagram. Several distinct phases are possible, separated by an XY-like and a p-state clocklike transition (p=2,3). The results are relevant for a number of systems that can be mapped onto coupled XY models.
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Granato et al. (1986) studied this question.
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