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Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules

Author

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  • Medved’, Igor
  • Trník, Anton
  • Huckaby, Dale A.

Abstract

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.

Suggested Citation

  • Medved’, Igor & Trník, Anton & Huckaby, Dale A., 2011. "Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3002-3019.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:17:p:3002-3019
    DOI: 10.1016/j.physa.2011.03.041
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