This is quite different from the case of freezing water to make ice. As you cool water, there will come a point when it suddenly crystallizes to form ice. This is an example of a phase transition. A ``phase transition'' occurs when a system undergoes a transformation from one phase to another. There are different types of phase transitions. Going from water to ice is an example of a ``first order phase transition.'' Typically a first order phase transition is associated with a latent heat and a volume change; ice expands. There are also second order phase transitions whose hallmark is a diverging thermodynamic quantity. When a paramagnet is cooled and becomes a ferromagnet (see the magnets on your refrigerator door for examples of a ferromagnet), it undergoes a second order phase transition and the magnetic susceptibility diverges. Another example of a second order phase transition is when an ordinary metal becomes a superconductor at low temperatures.
So we can rephrase our question about glasses and ask, ``Is the glass transition a phase transition?'' We can rule out the possibility of a first order phase transition since there is no latent heat or abrupt volume change. But could the glass transition be a second order phase transition? This has been a longstanding question for both physicists and chemists. Some have argued that there is no real phase transition; that a glass is simply a very, very viscous liquid. Others have speculated that it is a second order phase transition but the problem is that no one has been able to find a thermodynamic quantity that diverges.
Recently, my postdoc, Dr. Herve Carruzzo, and I have indeed found evidence that the glass transition is a second order phase transition. We have been performing numerical (molecular dynamics) simulations of a glass--forming liquid consisting of a mixture of big balls and little balls. We have found the first evidence of a diverging thermodynamic quantity. It is a rather esoteric quantity that is related to the nonlinear compressibility. The compressibility of a substance tells us how easy it is to change its volume. The higher the compressibility, the squishier it is. One way to measure the compressibility of a substance is to change the pressure on it and measure its change in volume. In fact one could plot the volume versus the pressure. If the plot were a straight line, minus the slope of this line would be the linear compressibility. For real materials the plot will be a curve which can be fit to a polynomial. The coefficient of the linear term is the linear compressibility; the coefficients of the nonlinear terms are the higher order compressibilities. At the glass transition the linear compressibility does not diverge but has a maximum. However, the nonlinear compressibilities do diverge, and this indicates that the glass transition is in fact a second order phase transition. So, in terms of our original question, glass may really be a solid after all.