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Via Monte Carlo studies of the frustrated XY or classical planar model wedemonstrate the possibility of a finite (nonzero) temperature spin/gauge glassphase in two dimensions. Examples of both periodic and quasiperiodic twodimensional lattices, where a high temperature paramagnetic phase changes to aspin/gauge glass phase with the lowering of temperature, are presented. Theexistence of the spin/gauge glass phase is substantiated by our study of thetemperature dependence of the Edwards-Anderson order parameter, spin glasssusceptibility, linear susceptibility and the specific heat. Finite sizescaling analysis of spin glass susceptibility and order parameter yields anonzero critical temperature and exponents that are in close agreement withthose obtained by Bhatt and Young in their random ${\pm J}$ Ising model studyon a square lattice. These results suggest that certain periodic andquasiperiodic two-dimensional arrays of superconducting grains in suitablychosen transverse magnetic fields should behave as superconducting glasses atlow temperatures.Comment: RevTex, 25 pages. 11 epsf figures available upon request  (rael@newton.physics.brocku.ca or bose@newton.physics.brocku.ca). Submitted  to Phys. Rev.

Possible two-dimensionalXYspin/gauge glasses on periodic and quasiperiodic lattices