Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules
✍ Scribed by Igor Medved’; Anton Trník; Dale A. Huckaby
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 419 KB
- Volume
- 390
- Category
- Article
- ISSN
- 0378-4371
No coin nor oath required. For personal study only.
✦ Synopsis
A convenient, Peierls-type approach to obtain low-temperature phases is to use the method of an m-potential. In this paper we show that, for more complex systems where it may be rather difficult to rewrite the Hamiltonian as an m-potential and whose configurations are subject to linear constraints, the verification of the Peierls condition can be reformulated as a linear programming problem. Before introducing this novel strategy for a general lattice system, we compare it with the m-potential method for a specific model molecular system consisting of an equimolar mixture of a chiral molecule and its non-superimposable mirror image that occupy all the sites of a honeycomb lattice. In one range of interactions, we prove that a racemic low-temperature phase occurs (containing equal numbers of each enantiomer). However, in a neighboring range of interactions, we show that a homochiral low-temperature phase (containing a single enantiomer) exists, and thus chiral segregation occurs in the system. Our linear programming technique yields these results in wider ranges of interactions than the m-potential method.