P. J. Kundrotas

On the Ising model for the simple cubic lattice

The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for a continuous phase transition and arguably the most studied model in theoretical physics. Since it was solved for a two-dimensional lattice by Onsager in 1944, thereby representing one of the very few exactly solvable models in dimensions higher than one, it has served as a testing ground for new developments in analytic treatment and numerical algorithms. Only series expansions and numerical approaches, such as Monte Carlo simulations, are available in three dimensions. This review focuses on Monte Carlo simulation. We build upon a data set of unprecedented size. A great number of quantities of the model are estimated near the critical coupling. We present both a conventional analysis and an analysis in terms of a Puiseux series for the critical exponents. The former gives distinct values of the high- and low-temperature exponents; by means of the latter we can get these exponents to be equal at the cost of having true asymptotic behaviour being found only extremely close to the critical point. The consequences of this for simulations of lattice systems are discussed at length.

Theoretical study of the oxygen-induced missing-row reconstruction on the Rh(110) surface

A microscopic model based on the Blume-Emery-Griffiths model is proposed to describe the missing-row reconstructions on the Rh(110) surface induced by oxygen. The phase diagram of the model at finite temperatures has been calculated employing the Monte Carlo and cluster variation methods. We find overall agreement between our results and the experimental data on the missing-row reconstruction for the ORh(110) surface as well as for other fcc (110) surfaces covered by atoms adsorbed in the threefold fcc hollow sites.

Modelling of Y and Cu substitution in : the effect on the oxygen ordering and superconducting temperature

The gradual destruction of the 60 K plateau in the dependence of due to the effects of substitutions of aluminium for the basal-plane copper and rare earths for yttrium is investigated. The calculations are performed using the percolation model relating the superconducting temperature to the oxygen ordering in the basal plane. The destruction of the plateau is related to changes in the structure of the orthorhombic phase. A small concentration of Al dopants is sufficient to cause a misorientation of the O - Cu - O chains and the disappearance of the phase ordering. Assuming that the coupling of spontaneous orthorhombic strain to the oxygen ordering is influenced by the substitution of rare earths for Y, we find that the phase region shrinks, and qualitatively describe the shift of the metal-to-insulator transition with the change of ionic radius of the substituent.

Holes amount and aging of quenched samples of YBa2Cu3O6 + x

Abstract The increase of the number of holes in the CuO 2 plane of YBa 2 Cu 3 O 6 + x during room temperature aging, Δp , is numerically calculated using the asymmetric next-nearest-neighbour interaction model. A maximum in the interval 0.35 x Δp ( x ) dependence. The position of this maximum depends on the annealing temperature. From a fit of the simulated data to experiment, a linear relation between T c and p is proposed. The number of holes is calculated using a simple chemical model for Al-doped YBa 2 Cu 3 O 6 + x compounds with the Al atoms ordered in the basal plane. It is demonstrated that the 3 × 3 and 4 × 4 Al ordering is favourable for superconductivity if the sample is free of Tb dopants.

Coulomb correlation gap : Finite-size analysis

Abstract A semiclassical model with randomly distributed N donor and K × N acceptor sites and with infinite-range Coulomb interaction is investigated by means of computer simulations on two-dimensional samples of different sizes. The shape of the Coulomb correlation gap in the density of one-electron excitations g ( e ) is obtained for different values of K within a wide energy interval around the Fermi energy μ . Using simple scaling arguments we demonstrate that the true behavior of g ( e ) in the immediate neighborhood of μ is hidden by the finite-size effects and find that g ( e ) further away from μ is described by a power-law with an exponent, depending on K and the sign of e − μ .

Ground-state study of a donor–acceptor model with finite charge-transfer energy

Abstract A donor–acceptor model with randomly distributed N donor and N acceptor sites and with finite charge transfer energy Δ is investigated at zero temperature by means of computer simulations on two-dimensional samples of different sizes. We demonstrate that the density of one-electron excitations g ( e ) for acceptors in the vicinity of the Fermi energy μ depends essentially on the size of the sample investigated and that g ( e ) further away from μ exhibits a size-independent power-law with the non-universal exponent decreasing with increasing Δ . Rigorous relations for μ and for the mapping of g ( e ) for donors into g ( e ) for acceptors are also given.

Coulomb gap in a model with finite charge-transfer energy

The Coulomb gap in a donor-acceptor model with finite charge-transfer energy Delta describing the electronic system on the dielectric side of the metal-insulator transition is investigated by means of computer simulations on two- and three-dimensional finite samples with a random distribution of equal amounts of donor and acceptor sites. Rigorous relations reflecting the symmetry of the model presented with respect to the exchange of donors and accepters are derived. In the immediate neighborhood of the Fermi energy mu. the single-particle density of states g(epsilon) is determined solely by finite size effects, and g(epsilon) further away from mu is described by an asymmetric power law with a nonuniversal exponent, depending on the parameter Delta.

Why does Y2Ba4Cu7O14+x not exhibit a plateau in its Tc(x) dependence? Predictions from oxygen ordering

Abstract On the basis of the ( T, x ) phase diagrams of oxygen ordering, the amounts of transferred holes n h as a function of x are calculated for pure as well as for doped samples of YBa 2 Cu 3 O 6+ x and Y 2 Ba 4 Cu 7 O 14+ x . These calculations allow us to anticipate the behavior of the superconducting temperature T c ( x ). In pure Y 2 Ba 4 Cu 7 O 14+ x a small kink is observed in n h ( x ) at x = 0.5, instead of the plateau characteristic to YBa 2 Cu 3 O 6+ x . Substitution of Cu in the basal plane by Al or removing Cu without substitution also leads to a smearing of the plateau.

Comparison of oxygen ordering and charge transfer in YBa2Cu3O6+x and Y2Ba4Cu7O14+x compounds

Abstract Various factors (orthorhombic strain, Cu-deficiency and Al-doping) which might be responsible for the disappearance of the plateau in the T c ( x ) dependence in YBa 2 Cu 3 O 6+ x are studied by Monte Carlo calculation of holes amount dependence on x in a framework of a generalized ASYNNNI model. These calculations allow us to explain the behaviour of the superconducting temperature T c ( x ).