Limit shapes in the double-Ising model
Presenter
February 24, 2012
Keywords:
- mathematical statistical mechanics
- percolation
- probability theory
- phase transitions
- scaling laws
- SLE
- Ising model
- amoeba
- tropical geometry
MSC:
- 82C20
- 82C26
- 82C27
- 82C05
- 82C44
- 82C43
- 82Cxx
- 82-xx
Abstract
We describe a naturally-occurring 3-parameter family of measures on double-Ising configurations on Z^2 obtained by conditioning on spin domain boundary connections. We formulate an appropriate variational principle and discuss the relevant limit shape formation.