2011 | OriginalPaper | Chapter
Clustering in Interfering Binary Mixtures
Authors : Sarah Miracle, Dana Randall, Amanda Pascoe Streib
Published in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Publisher: Springer Berlin Heidelberg
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Colloids are binary mixtures of molecules with one type of molecule suspended in another. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters. We characterize the high and low density phases for a general family of discrete
interfering binary mixtures
by showing that they exhibit a “clustering property” at high density and not at low density. The clustering property states that there will be a region that has very high area to perimeter ratio and very high density of one type of molecule. A special case is mixtures of squares and diamonds on ℤ
2
which corresond to the Ising model at fixed magnetization.