[Phase transition] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Phase transition
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Posted by: Todd Rowland
Do you think this counts as a phase transition?
ArrayPlot[CellularAutomaton[45, {{1}, {0, 0, 1}}, 130]]
It is the picture on http://www.wolframscience.com/nksonline/page-701
Posted by: Lawrence J. Thaden
But it is a system with such a small number of particles...
"Phase transitions happen when the free energy of a system is non-analytic for some choice of thermodynamic variables - see phases. This non-analyticity generally stems from the interactions of an extremely large number of particles in a system, and does not appear in systems that are too small."
http://en.wikipedia.org/wiki/Phase_transition
Posted by: Alexandre Ismail
I say "yes". What LJT refers to for a definition of phase transition is still based on a continuous way of looking at systems. That point of view really likes huge numbers of particles because it makes the continuous viewpoint more plausible as an approximation to the discrete underlying reality.
I'd say, sure, it is a phase transition because over a border of 1 cell (the minimum size in the given system) you've got two rather different types of behaviour. One might say its not (or "less of"?) a phase transition if the transition from 1 behaviour to another was spread out over a noisy border region several cells wide.
The definition LJT refers to, I think, is a formalism for defining phase transitions in that style of thinking. I guess it is useful in some sense to define formation of ice from water analytically. But basically, ice is water when it gets hard. Easy!
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