  We discuss a simple model based on the Minority Game which reproduces the
main stylized facts of anomalous fluctuations in finance. We present the
analytic solution of the model in the thermodynamic limit and show that
stylized facts arise only close to a line of critical points with non-trivial
properties. By a simple argument, we show that, in Minority Games, the
emergence of critical fluctuations close to the phase transition is governed by
the interplay between the signal to noise ratio and the system size. These
results provide a clear and consistent picture of financial markets as critical
systems.
