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More recently STM experimets present firm evidence of some kind of chargemodulation in underdoped cuprates. The peculiar observations of the aboveexperiments are located in the so called pseudo-gap region of the phasediagram, just over the superconducting-dome. The model that will be usedcaptures in a simple way the idea that the pseudo-gap phase is formed of boundfermion pairs which are close to a CDW instability but generally do not havelong range order due to quenched disorder. Thus the charge degrees of freedomwill be modeled by an Ising order parameter in the presence of quencheddisorder, so representing a charge glassy phase. This glassy phase will be incompetition with a superconducting phase modeled by a complex order parameter.As a first step we will study the model in one dimension without disorder tofamiliarize with it and also to search for a possible explanation of the GiantProximity Effect (GPE). After that we will investigate numerically the groundstate properties of the 2-dimensional lattice model, focusing our attentionespecially on the stiffness and magnetization of the system in the xy plane. Wewill show that disorder can induce superconductivity in a CDW phase. Thispicture is really interesting because it could show how an insulating systemcan produce a superconducting phase thank to the interplay with impurites.

Competition between Superconductivity and Charge Density Waves: the Role of Disorder