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...

We consider a three-component model of rodlike molecules AA, BB, and AB, confined to the bonds of the honeycomb or three-coordinated Bethe lattice, and with three-body interactions between the molecular ends near a common lattice site. The model is equivalent to an Ising model on an associated...

The Pirogov–Sinai theory of phase transitions is used to prove the existence of ordered molecular phases at low temperatures in statistical mechanical models for several types of molecular systems. A three-dimensional lattice gas containing two molecular mirror images (enantiomers) was proved...

A statistical mechanical model for the phase transition from disordered ice VII to ordered ice VIII is introduced. The model includes steric repulsions between neighboring atoms on different hydrogen-bonded structures. These repulsions can be reduced by small displacements of neighboring...

A ternary solution is considered in which molecules of types AA, BB, and AB occupy the bonds of a honeycomb lattice or a three-coordinate Bethe lattice. The three molecular ends near a common lattice site interact with arbitrary three-body interactions εAAA, εAAB, εABB and εBBB. The model is...

A model three-component system is considered in which the bonds of a lattice are covered by rodlike molecules of types AA, BB, and AB. The ends of molecules near a common lattice site interact with energies ϵAA, ϵBB, and ϵAB. The exact two-phase coexistence surface in temperature-composition...

We consider random walks on one-dimensional random channels between two absorbing barriers. The problem can perhaps be used to model the diffusion of a molecule in a “random” membrane, the molecule traversing a random channel formed by the constituent membrane molecules. We are able to...