Control of a qubit state by a soliton propagating through a Heisenberg spin chain.

We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a Hamiltonian involving the interaction between the soliton and the qubit. We show that under certain conditions the generic Hamiltonian may be mapped on that of a qubit two-level system with matrix elements depending on the soliton parameters. We considered the action of a bright and a dark soliton depending on the driving nonlinear wave function. We considered a local interaction restricted the closest to the qubit spin in the chain. We computed the expressions of the physical quantities of interest for all cases and analyzed their behavior in some special limits.

Molecular magnetism in the multi-configurational self-consistent field method.

We develop a structured theoretical framework used in our recent articles (2019 Eur. Phys. J. B 92 93 and 2020 Phys. Rev. B 101 094427) to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic susceptibility of the molecular magnet Ni4Mo12. The theoretical background is based on the molecular orbital theory in conjunction with the multi-configurational self-consistent field method and results in a post-Hartree-Fock scheme for constructing the corresponding energy spectrum. Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete coupling parameters accounting for the relevant spectroscopic magnetic excitations, magnetization and magnetic susceptibility. The explicit expressions of the eigenenergies of the ensuing Hamiltonian are determined and the physical origin of broadening and splitting of experimentally observed peaks in the magnetic spectra is discussed. To demonstrate the efficiency of our method we compute the spectral properties of a spin-one magnetic dimer. The present approach may be applied to a variety of magnetic units based on transition metals and rare Earth elements.

Topological transitions in two-dimensional lattice models of liquid crystals.

The phase diagram of hard-core nematogenic models in three-dimensional space can be studied by means of Onsager's theory, and, on the other hand, the critical properties of continuous interaction potentials can be investigated using the molecular field approach pioneered by Maier and Saupe. Comparison between these treatments shows a certain formal similarity, reflecting their common variational root; on this basis, hard-core potential models can be mapped onto continuous ones, via their excluded volume. Some years ago, this line of reasoning had been applied to hard spherocylinders, hence the continuous potential G(tau)=a+bsqrt[1-tau{2}], b>0 had been used to define a mesogenic model on a three-dimensional lattice [S. Romano, Int. J. Mod. Phys. B 9, 85 (1995)]; in the formula, tau denotes the scalar product between the two unit vectors defining particle orientations. Here we went on by addressing the same interaction potential on a two-dimensional lattice. Our analysis based on extensive Monte Carlo simulations found evidence of a topological transition, and the critical behavior in its vicinity was studied in detail. Results obtained for the present model were compared with those already obtained in the literature for interaction potentials defined by Legendre polynomials of second and fourth orders in the scalar product tau.

Critical Casimir forces for O(n) systems with long-range interaction in the spherical limit.

We present exact results on the behavior of the thermodynamic Casimir force and the excess free energy in the framework of the d -dimensional spherical model with a power law long-ranged interaction decaying at large distances r as r(-d-sigma) , where sigma T(c) and T< T(c) . The universal finite-size scaling function governing the behavior of the force in the critical region is derived and its asymptotics are investigated. While in the critical and subcritical region the force is of the order of L(-d) , for T> T(c) it decays as L(-d-sigma) , where L is the thickness of the film. We consider both the case of a finite system that has no phase transition of its own, when d-1sigma , when one observes a dimensional crossover from d to a d-1 dimensional critical behavior. The behavior of the force along the phase coexistence line for a magnetic field H=0 and T< T(c) is also derived. We have proven analytically that the excess free energy is always negative and monotonically increasing function of T and H . For the Casimir force we have demonstrated that for any sigma > or =1 it is everywhere negative, i.e., an attraction between the surfaces bounding the system is to be observed. At T= T(c) the force is an increasing function of T for sigma>1 and a decreasing one for sigma<1 . For any d and sigma the minimum of the force at T= T(c) is always achieved at some H unequal to 0 .

Finite-size scaling in disordered systems.

The critical behavior of a quenched random hypercubic sample of linear size L is considered, within the "random-T(c)" field-theoretical model, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension d=4-epsilon and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.

Scaling behavior for finite O(n) systems with long-range interaction.

A detailed investigation of the scaling properties of the fully finite O(n) systems, under periodic boundary conditions, with long-range interaction, decaying algebraically with the interparticle distance r like r(-d-sigma), below their upper critical dimension, is presented. The computation of the scaling functions is done to one loop order in the nonzero modes. The results are obtained in an expansion of powers of sqrt[epsilon], where epsilon=2sigma-d up to O(epsilon(3/2)). The thermodynamic functions are found to depend upon the scaling variable z=RU(-1/2)L(2-eta-epsilon/2), where R and U are the coupling constants of the constructed effective theory, and L is the linear size of the system. Some simple universal results are obtained.