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Self-Dual Vortices in Abelian Higgs Models with Dielectric Function on the Noncommutative Plane

We show that Abelian Higgs Models with dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for the usual $U(1)$ model and for the $SU(2)\times U(1)$ semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behaviour when the noncommutativity parameter tends to zero results in this way considerably enlarged.