Kirkpatrick and co-workers found that the computer algorithms used to solve NP-complete problems can undergo sudden phase transitions as the various criteria used to search for a solution are varied. The solutions get harder to find at the onset of the phase transition - as the search 'freezes' - and then easier again once the system has passed through the phase transition. The team noticed that if the phase transition is abrupt, like the freezing phase transition, the problem is exponentially hard. However, if the transition is continuous, like the demagnetization of iron when heated, then the problem is only polynomially hard.