When water boils, it undergoes a phase transition from a liquid to a gas phase. The equation of state in each of these phases is simply a regular function, continuous with continuous derivatives; except in going from one phase to another it abruptly changes to a different regular function. The liquid gas transition is simply a first order phase transition, in that the first derivative of the Gibbs potential is discontinuous across the phase boundary. There are second order phase transitions, in which the first derivatives of G are continuous, except the second derivatives change discontinuously. Examples include the gas-liquid transition at the critical point, the ferromagnetic transition and the superconducting transition . . Many important problems of complexity are related in one way or another with the presents of phase transition phenomena. Most complex systems are known to potentially display a number of different patterns of qualitative behavior of phases. Such phases correspond to different forms of internal organization and two given phases are usually separated by a sharp boundary and crossing such a frontier implies a change in system level behavior. Many systems exist in multiple phases, depending on the values of external parameters like temperature, pressure etc. A phase transition occurs when there is simply a singularity in the free energy or one of its derivatives. What is often visible is simply a sharp change in the properties of a substance. The transitions from liquid to gas, from a normal conductor to a superconductor or from paramagnet to ferromagnet are common examples. As the temperature and pressure are varied water can exist as a solid, a liquid or a gas. Well defined phase boundaries separate the regions in which each state is stable. Crossing the phase boundaries there is simply a jump in the density and a latent heat, signatures of a first order transition .