No abstract

Abstract. A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some ρ > 0, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals one). The surface susceptibility χ 1,1 has been evaluated exactly. For ρ = 1 we find that χ 1,1 is finite at the bulk critical temperature T c , in contrast with the recently derived value γ 1,1 = 1 in the case of just one global spherical constraint. The result γ 1,1 = 1 is recovered only if ρ = ρ c = 2 − (12K c ) −1 , where K c is the dimensionless critical coupling. When ρ > ρ c , χ 1,1 diverges exponentially as T → T + c . An effective hamiltonian which leads to an exactly solvable model with γ 1,1 = 2, the value for the n → ∞ limit of the corresponding O(n) model, is proposed too.

The spin-s one dimensional Ising model is studied analytically within the framework of transfer matrix method. Exact results for some thermodynamical properties such as the internal energy, the entropy, the magnetization and the magnetic susceptibility are obtained for general spin-s in the absence (presence) of a magnetic field. The critical behavior of the thermodynamical properties are analysed for some values of spin-s (1/2, 1 and 3/2) at different temperature and field. The asymptotic behavior of these properties are investigated especially close to the critical temperature T → 0 and when T → ∞.

In this paper, we investigate the entanglement degree in the interaction of a two-level atom prepared in a momentum eigenstate with an additional Stark-shift. We use the quantum entropy as a measure of the entanglement degree. The constants of motion and the density matrix of the system are obtained. The effect of the detuning and the Stark-shift parameters when the atom is prepared initially in the upper state are investigated. It is found that the detuning and the Stark shift affected on the entanglement of the atomic system, and the influence of the center-of-mass motion play an important role in the entanglement degree.

The one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.