Azer Kerimov - Academia.edu (original) (raw)

Papers by Azer Kerimov

Communications in Mathematical Physics, 1997

We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in ... more We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast.

Theoretical and Mathematical Physics, Mar 1, 1984

Journal of Mathematical Physics, Oct 1, 1999

Springer eBooks, 1991

We consider the Izing antiferromagnet on the one dimensional lattice with long-range interaction.

Theoretical and Mathematical Physics, 1984

Journal of Mathematical Physics, 1999

Uniqueness of Gibbs states in the one-dimensional antiferromagnetic model with very long-range in... more Uniqueness of Gibbs states in the one-dimensional antiferromagnetic model with very long-range interaction is established.

Discrete Mathematics, Dec 1, 2015

Let C (n, m) be a n ×m chessboard. An ascending (respectively descending) staircase walk on C (n,... more Let C (n, m) be a n ×m chessboard. An ascending (respectively descending) staircase walk on C (n, m) is a rook's path on C (n, m) that in every step goes either right or up (respectively right or down). We determine the minimal number of ascending and descending staircase walks covering C (n, m).

Journal of Mathematical Physics

One-dimensional long-range Ising models with antiferromagnetic, convex pair interactions are inve... more One-dimensional long-range Ising models with antiferromagnetic, convex pair interactions are investigated. A new criterion characterizing ground states is given. The criterion and a new transformation yield short proofs identifying and characterizing the ground states. The uniqueness of periodic ground states up to shifts is shown.

Physica A: Statistical Mechanics and its Applications, 1999

A one-dimensional model with two spin variables having a unique ground state and at least two ext... more A one-dimensional model with two spin variables having a unique ground state and at least two extreme limit Gibbs states is constructed.

Rocky Mountain Journal of Mathematics, 2020

We investigate a Markov chain with a state space 1, 2,. .. , r stopping at appearance of patterns... more We investigate a Markov chain with a state space 1, 2,. .. , r stopping at appearance of patterns consisting of two consecutive states. It is observed that the expected stopping times of the chain have surprising oscillating dependencies on starting positions. Analogously, the stopping probabilities also have oscillating dependencies on terminal states. In a nonstopping Markov chain the frequencies of appearances of two consecutive states are found explicitly.

Journal of Statistical Mechanics: Theory and Experiment, 2014

We extend a condition for the uniqueness of Gibbs states in terms of percolation in the coupling ... more We extend a condition for the uniqueness of Gibbs states in terms of percolation in the coupling of two independent realizations to lattice spin models with long-range interactions and a not necessarily unique ground state.

International Journal of Modern Physics B, 2003

We consider one-dimensional models of classical statistical physics and prove that at each fixed ... more We consider one-dimensional models of classical statistical physics and prove that at each fixed value of the temperature for all realizations of additional sufficiently strong random external field the limiting Gibbs state is unique.

International Journal of Modern Physics B, 2009

We consider the one-dimensional ferromagnetic Ising model with very long range interaction under ... more 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.

Physica A: Statistical Mechanics and its Applications, 1996

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

Physica A: Statistical Mechanics and its Applications, 1998

Uniqueness of limit Gibbs states of one dimensional models with a unique "stable" ground state is... more Uniqueness of limit Gibbs states of one dimensional models with a unique "stable" ground state is established at low temperatures.

Physica A: Statistical Mechanics and its Applications, 2012

We consider the one-dimensional ferromagnetic Ising model with very long-range interaction under ... more 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.

Modern Physics Letters B, 2007

The absence of phase transitions in one-dimensional Widom–Rowlinson model with long-range interac... more 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.

Modern Physics Letters B, 2012

A zero-temperature phase-diagram of the one-dimensional ferromagnetic Ising model is investigated... more 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 field are identically oriented.

Journal of Statistical Physics, 1988

For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that ... more For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.