# Modeling Trends in Long-Term IT as a Phase Transition

The most reasonable model for our faster-than-exponential growth in long-term IT trends is that of a phase transition.

At a second-order phase transition, the heat capacity becomes discontinuous.

The heat capacity image is provided courtesy of a wikipedia site on heat capacity transition(s).

L. Witthauer and M. Diertele present a number of excellent computations in graphical form in their paper The Phase Transition of the 2D-Ising Model.

There is another interesting article by B. Derrida & D. Stauffer in Europhysics Letters, Phase Transitions in Two-Dimensional Kauffman Cellular Automata.

The divergent increase in heat capacity is similar in form to the greater-thean-exponential increase in IT measurables, as discussed in my previous post, Going Beyond Moore’s Law and identified in Super-exponential long-term trends in IT.

In one of my earlier posts, starting a modeling series on phase transitions from metastable states (using the Ising model with nearest-neighbor interactions and simple entropy), I identified a key challenge in identifying what it was that we were attempting to model. That is, What is *x*?. When we identify what it is that we are trying to model, we can figure out the appropriate equations.

Now, we have the same problem – but in reverse! We have an equation – actually, an entire modeling system (the Ising spin-glass model works well) – that gives us the desired heat capacity graphs. What we have to figure out now is: What is it exactly that is being represented if we choose the “phase transition analogy” for interpreting our faster-than-exponential growth in IT (and in other realms of human experience)?

That will be the subject of a near-term posting.

(Another good heat capacity graph is viewable at: http://physics.tamuk.edu/~suson/html/3333/Degenerate_files/image108.jpg)