Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).
Thought of as sites either occupied or vacant (1/0) on a lattice, it is a model for the liquid-gas transition: dense regions of occupied "liquid" are surrounded by dilute regions of mostly "gas". Our simulation isn't ideal for visualizing this, because we allow atoms to be created and destroyed: one of the possible projects involves writing a version which only allows sites to flip in pairs, moving atoms from occupied to empty sites. Try running at 2.4 for a while (to generate a "clumped up" state), and then drop to 2.0 or so. For a limited time, you will likely observe fairly well defined red regions and white regions: think of a red fluid with a few red vapor atoms in the white regions. As you run for longer, you'll see either the vapor or the fluid win: the last drop will evaporate, or the last bubble will collapse. Of course, real liquid/vapor transitions are in three dimensions: another project will be to write a version of the program which runs a three-dimensional Ising model.
James P. Sethna, sethna@lassp.cornell.edu, https://sethna.lassp.cornell.edu/sethna.html
Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).