This week’s BMC post will be a bit of a short, focused post about phase transitions and a nifty mathematical tool for looking at how they behave.  I’m in the foggy head space of 4 hours of sleep right now, so forgive me if this is less of a science primer and more the ramblings of a madman.

Phase Transitions

You are probably all familiar with the concept of phase transitions in the chemical sense: solids, liquids, and gases changing from one form to another.  This is just one type of phase transition, all of which can be described as a rapid shift of the majority of particles in the microscopic view of a system that causes an observable, macroscopic change.  Classic examples of phase transitions other than the ones I discussed earlier is the loss of magnetization as a magnet is heated to the Curie point, the transition of a liquid to a superfluid, and the appearance of superconductivity.

Critical Exponents

For every phase transition, there is a critical temperature at which the phase transition occurs.  Once this temperature is reached, there is a cascade, in which the majority of particles change their state, and a rapid macroscopic change is observed.  For a number of macroscopic properties, there is a power-law relation between the ratio of the temperature distance to the critical temperature and the critical temperature itself, and the property being observed.  This power law relation stays flat and mostly linear for large distances from the critical temperature, but craters rapidly as the critical temperature is approached.  A different exponent is used for different properties, but the behavior is the same.  Magnetization, solid cohesion, specific heat, and numerous other physical properties all have this behavior.  So, if you are ever heating or cooling a system and the property you are measuring explodes or craters, you are probably approaching a phase transition.  This effect is what makes phase transitions so rapid and seemingly black and white (solid to liquid, no in between “sliquid”, etc.)