High Tc Superconductivity and Magnetism in t-J and t-t''-J Models

In the last few years, the use of numerical methods as Monte Carlo, stochastic models and strongly correlated systems close to phase transitions, has increased exponentially with unexpected success also in fields really faraway from physics as for example biology, chemistry, finance, sociology and climatology. In this book we expose a new Monte Carlo variational approach applied to t-J and t-t''-J Models for describing the experimental phase diagram of the High-Tc Superconductors that after more than 20 years is still an open and amazing problem. We focused our analysis on phase separation, d-wave superconductivity and magnetic properties and thanks to our method we were able to describe the main experimental results on the phase diagrams of the High-Tc materials, highlighting the key factors involved which are at the basis of their strange behaviour. This work should be especially useful to all scientists interested in strongly correlated systems and numerical methods as starting point for further studies on High-Tc superconductors or for PhD courses with the target of introduce to numerical methods and their applications to correlated systems.