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An effective free energy of a two dimensional (i.e. large area) JosephsonJunctions is derived, allowing for thermal fluctuations, for random magneticfields and for external currents. We show by using replica symmetry breakingmethods, that the junction has four distinct phases: disordered, Josephsonordered, a glass phase and a coexisting Josephson order with the glass phase.Near the coexistence to glass transition at s=1/2 the critical current is ~(area)^{-s+1/2} where s is a measure of disorder. Our results may account forjunction ordering at temperatures well below the critical temperature of thebulk in high T_c trilayer junctions.Comment: 21 pages including 2 ps figures, Revtex. Minor corrections in text,  erratum added on last pag

Erratum: Disorder in two-dimensional Josephson junctions [Phys. Rev. B55, 14 499 (1997)]