Browsing by Subject "Extreme Gibbs state"

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    Absence of phase transitions in one-dimensional antiferromagnetic models with long-range interactions
    (Kluwer Academic Publishers-Plenum Publishers, 1993) Kerimov, A.
    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 ground states and typical configurations is given. © 1993 Plenum Publishing Corporation.
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    A condition for the uniqueness of Gibbs states in one-dimensional models
    (Elsevier BV * North-Holland, 1998) Kerimov, A.
    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.
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    On the uniqueness of Gibbs states in the Pirogov-Sinai theory
    (World Scientific Publishing Co. Pte. Ltd., 2006) Kerimov, A.
    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 or Gertzik-Pirogov-Sinai condition. The Pirogov-Sinai theory describes the phase diagrams of these models at low temperature regimes. By using the method of doubling and mixing of partition functions we give an alternative elementary proof of the uniqueness of limiting Gibbs states at low temperatures in ground state uniqueness region. © World Scientific Publishing Company.
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    One-dimensional long-range ferromagnetic ising model under weak and sparse external field
    (2009) Kerimov, A.
    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 state. © 2009 World Scientific Publishing Company.
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    The one-dimensional long-range ferromagnetic Ising model with a periodic external field
    (Elsevier, 2012) Kerimov, A.
    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 Gibbs state. © 2012 Elsevier B.V. All rights reserved.