Abstract
It is shown that Peierls' argument can be extended to prove the coexistence of states which can be transformed into each other only by reflection, inversion or rotation. This makes Peierls' argument applicable to the repulsive lattice gas on a large class of lattices, as well as many models for liquid crystals, ferroelectrics etc. It is specifiquely shown how the argument can be applied to a lattice gas with nearest neighbour repulsion on the hexagonal lattice and the diamond lattice.
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