Browsing by Subject "Hamiltonian"

Now showing 1 - 9 of 9

Open Access
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.
Open Access
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.
Open Access
Gibbs measures and phase transitions in one-dimensional models
(2000) Mallak, Saed
In this thesis we study the problem of limit Gibbs measures in one-dimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for one-dimensional models. VVe construct a one-dimensional model disproving a uniqueness conjecture formulated before for one-dimensional models. It turns out that this conjecture is correct under some natural regularity conditions. VVe also apply the uniqueness theorem to some one-dimensional models.
Open Access
Ground states of one-dimensional long-range ferromagnetic ising model with external field
(World Scientific Publishing, 2012) Kerimov, A.
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. © 2012 World Scientific Publishing Company.
Open Access
Limiting Gibbs measures in some one and two dimensional models
(2005) Tülü, Serdar
We give the definitions of finite volume Gibbs measure and limit Gibbs states. In one dimensional Ising model with arbitrary boundary conditions we calculate correlation functions in explicit way. In one dimension, conditions for uniqueness of Gibbs state are considered. We also discuss two dimensional Ising model.
Open Access
Limiting Gibbs measures of some models of classical statistical mechanics
(2002) Ünal, Deniz
We consider some models of classical statistical mechanics with their random perturbations and investigate the phase diagrams of this models. By using uniqueness theorem we prove the absence of phase transitions in this models.
Open Access
Phase transition in one dimensional model with unique ground state
(Elsevier BV * North-Holland, 1996) Kerimov, A.
A one - dimensional model having a unique ground state and admitting a phase transition is constructed.
Open Access
Triplets of closely embedded Dirichlet type spaces on the unit polydisc
(Birkhaeuser Science, 2013) Cojuhari, P.; Gheondea, A.
We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted L2 spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces Dα(DN) of holomorphic functions on the unit polydisc DN and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space H2(DN) through a scale of Dirichlet type spaces and Bergman type spaces. © 2012 Springer Basel.
Open Access
Triplets of closely embedded Hilbert spaces
(Springer, 2014) Cojuhari, P.; Gheondea, A.
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. We provide a model and an abstract theorem as well for a triplet of closely embedded Hilbert spaces associated to positive selfadjoint operator H, that is called the Hamiltonian of the system, which is supposed to be one-to-one but may not have a bounded inverse. Existence and uniqueness results, as well as left-right symmetry, for these triplets of closely embedded Hilbert spaces are obtained. We motivate this abstract theory by a diversity of problems coming from homogeneous or weighted Sobolev spaces, Hilbert spaces of holomorphic functions, and weighted L2 spaces. An application to weak solutions for a Dirichlet problem associated to a class of degenerate elliptic partial differential equations is presented. In this way, we propose a general method of proving the existence of weak solutions that avoids coercivity conditions and Poincaré–Sobolev type inequalities. © 2014, Springer Basel.