Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules |
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Authors: | Igor Medved’ Anton Trník Dale A Huckaby |
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Institution: | a Department of Physics, Constantine the Philosopher University, 94974 Nitra, Slovakiab Department of Materials Engineering and Chemistry, Czech Technical University, 16629 Prague, Czech Republicc Department of Chemistry, Texas Christian University, Fort Worth, TX 76129, United States |
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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. |
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Keywords: | Low-temperature phases Ground states Peierls condition Chiral molecules |
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