Colloids, Lattice Gasses, and Other Models with Hard Constraints
Presenter
February 22, 2012
Keywords:
- mathematical statistical mechanics
- percolation
- probability theory
- phase transitions
- scaling laws
- SLE
- Ising model
- colloids
- clustering
MSC:
- 82C20
- 82C26
- 82C27
- 82C05
- 82C44
- 82C43
- 82Cxx
- 82-xx
Abstract
Colloids are binary mixtures of molecules with one type of molecule suspended in another where all non-overlapping arrangements are equally likely. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters, suggesting a phase transition occurs as the density of both types of molecules increases. In this talk we will discuss various strategies for sampling configurations of non-overlapping particles including lattice gasses and colloids in order to gain empirical evidence of this conjecture. Then we will show how to characterize the two phases for a general family of "interfering colloid models" by demonstrating that they exhibit a "clustering property" at high density and not at low density. The clustering property holds when there is a region with very high area to perimeter ratio and very high density of one type of molecule. A special case of interfering colloids is mixtures of squares and diamonds on Z^2, which correspond to the Ising model at fixed magnetization.