Uniqueness of limit Gibbs states of one dimensional models with a unique "stable" ground state is established at low temperatures. © 1998 Elsevier Science B.V. All rights reserved.

We consider the one-dimensional ferromagnetic Ising model with very long range interaction under weak and sparse biased external field and prove that at sufficiently low temperatures, the model has a unique limiting Gibbs ...

The absence of phase transitions in a one-dimensional model with long-range antiferromagnetic potential is established at low temperatures when the ground states have a rational density. A description of the set of all ...

A zero-temperature phase-diagram of the one-dimensional ferromagnetic Ising model is investigated. It is shown that at zero temperature spins of any compact collection of lattice points with identically oriented external ...

We consider models of classical statistical mechanics satisfying natural stability conditions: a finite spin space, translation-periodic finite potential of finite range, a finite number of ground states meeting Peierls ...

The absence of phase transitions in one-dimensional Widom-Rowlinson model with long-range interaction is established in the non-symmetric case when different particles have different activity parameters. © World Scientific ...

We consider the one-dimensional ferromagnetic Ising model with very long-range interaction under a periodic, biased and weak external field and prove that at sufficiently low temperatures the model has a unique limiting ...

A one - dimensional model having a unique ground state and admitting a phase transition is constructed.