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We address the existence and stability of localized modes in thetwo-dimensional (2D) linear Schroedinger lattice with two symmetric nonlinearsites embedded into it, and a generalization for moderately localizednonlinearity featuring two distinct symmetric maxima. The latter setting admitsa much greater variety of localized modes. Symmetric, antisymmetric, andasymmetric discrete solitons are found, and a subcritical bifurcation,accounting for the spontaneous symmetry breaking (SSB) of the symmetric modesand transition to asymmetric ones, is identified. Existence and stability ofmore complex 2D solutions in the form of discrete symmetric and asymmetricvortices are also discussed.

Localized modes in two-dimensional Schroedinger lattices with a pair of nonlinear sites