26 research outputs found
Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions
In a previous paper [Phys. Rev. E 90, 022506 (2014)], we had studied
thermodynamic and structural properties of a three-dimensional simple-cubic
lattice model with dipolar-like interaction, truncated at nearest-neighbor
separation, for which the existence of an ordering transition at finite
temperature had been proven mathematically; here we extend our investigation
addressing the full-ranged counterpart of the model, for which the critical
behavior had been investigated theoretically and experimentally. In addition
the existence of an ordering transition at finite temperature had been proven
mathematically as well. Both models exhibited the same continuously degenerate
ground-state configuration, possessing full orientational order with respect to
a suitably defined staggered magnetization (polarization), but no nematic
second-rank order; in both cases, thermal fluctuations remove the degeneracy,
so that nematic order does set in at low but finite temperature via a mechanism
of order by disorder. On the other hand, there were recognizable quantitative
differences between the two models as for ground-state energy and critical
exponent estimates; the latter were found to agree with early Renormalization
Group calculations and with experimental results.Comment: 9 pages, 10 figures, accepted for publication in the Physical Review
E. arXiv admin note: substantial text overlap with arXiv:1408.473
Exact results for some Madelung type constants in the finite-size scaling theory
A general formula is obtained from which the madelung type constant: extensively used in the finite-size
scaling theory is computed analytically for some particular cases of the
parameters and . By adjusting these parameters one can obtain
different physical situations corresponding to different geometries and
magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added
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Linear and ring polymers in confined geometries
A short overview of the theoretical and experimental works on the polymer-colloid mixtures is given. The behaviour of a dilute solution of linear and ring polymers in confined geometries like slit of two parallel walls or in the solution of mesoscopic colloidal particles of big size with different adsorbing or repelling properties in respect to polymers is discussed. Besides, we consider the massive field theory approach in fixed space dimensions d = 3 for the investigation of the interaction between long flexible polymers and mesoscopic colloidal particles of big size and for the calculation of the correspondent depletion interaction potentials and the depletion forces between confining walls. The presented results indicate the interesting and nontrivial behavior of linear and ring polymers in confined geometries and give possibility better to understand the complexity of physical effects arising from confinement and chain topology which plays a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells. The possibility of using linear and ring polymers for production of new types of nano- and micro-electromechanical devices is analyzed
Possible zero sound in layered perovskites with ferromagnetic - exchange interaction
We analyze the conditions for observation of zero sound in layered
perovskites with transition metal ion on chalcogenide oxidizer. We conclude
that propagation of zero sound is possible only for anti-ferromagnetic sign of
the - interaction. If the - exchange integral has
antiferromagnetic sign, as it is perhaps in the case for layered cuprates, zero
sound is a thermally activated dissipation mode,which generates only "hot
spots" in the Angle Resolved Photoemission Spectroscopy (ARPES) data along the
Fermi contour. We predict that zero sound will be observable for transition
metal perovskites with 4 and 3 levels close to the -level of the
chalcogenide. The simultaneous lack of superconductivity, the appearance of hot
spots in ARPES data, and the proximity of the three named levels, represents
the significant hint for the choice of material to be investigated.Comment: 7 pages, 4 figures, 30 reference
Hot spots along the Fermi contour of high- cuprates analyzed by - exchange interaction
We perform a thorough theoretical study of the electron properties of a
generic CuO plane in the framework of Shubin-Kondo-Zener - exchange
interaction that simultaneously describes the correlation between and the
Cu4 energy. To this end, we apply the Pokrovsky theory [J. Exp. Theor. Phys.
13, 447-450 (1961)] for anisotropic gap BCS superconductors. It takes into
account the thermodynamic fluctuations of the electric field in the dielectric
direction perpendicular to the conducting layers. We microscopically derive a
multiplicatively separable kernel able to describe the scattering rate in the
momentum space, as well as the superconducting gap anisotropy within the BCS
theory. These findings may be traced back to the fact that both the Fermi
liquid and the BCS reductions lead to one and the same reduced Hamiltonian
involving a separable interaction, such that a strong electron scattering
corresponds to a strong superconducting gap and vice versa. Moreover, the
superconducting gap and the scattering rate vanish simultaneously along the
diagonals of the Brillouin zone. We would like to stress that our theoretical
study reproduces the phenomenological analysis of other authors aiming at
describing Angle Resolved Photoemission Spectroscopy measurements. Within
standard approximations one and the same - exchange Hamiltonian describes
gap anisotropy of the superconducting phase and the anisotropy of scattering
rate of charge carriers in the normal phase.Comment: 10 pages, 3 figures, 56 reference
Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling
The quantum rotors model can be regarded as an effective model for the
low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we
consider a -dimensional model in the spherical approximation confined to a
general geometry of the form (
-linear space size and -temporal size) and subjected to periodic
boundary conditions. Due to the remarkable opportunity it offers for rigorous
study of finite-size effects at arbitrary dimensionality this model may play
the same role in quantum critical phenomena as the popular Berlin-Kac spherical
model in classical critical phenomena. Close to the zero-temperature quantum
critical point, the ideas of finite-size scaling are utilized to the fullest
extent for studying the critical behavior of the model. For different
dimensions and a detailed analysis, in terms of the
special functions of classical mathematics, for the susceptibility and the
equation of state is given. Particular attention is paid to the two-dimensional
case.Comment: 33pages, revtex+epsf, 3ps figures included submitted to PR
An Exchange Mechanism for the Magnetic Behavior of Er3+ Complexes
We study the magnetic properties of the erbium based compounds, Na9[Er(W5O18)2] and [(Pc)Er{Pc{N(C4H9)2}8}]·/−, in the framework of an effective spin exchange model involving delocalized electrons occupying molecular orbitals. The calculations successfully reproduce the experimental data available in the literature for the magnetic spectrum, magnetization and molar susceptibility in dc and ac fields. Owing to their similar molecular geometry, the compounds’ magnetic behaviors are interpreted in terms of the same set of active orbitals and thus the same effective spin coupling scheme. For all three complexes, the model predicts a prompt change in the ground state from a Kramer’s doublet at zero fields to a fully polarized quartet one brought about by the action of an external magnetic field without Zeeman splitting. This alteration is attributed to the enhancement of the effect of orbital interactions over the spin exchange as the magnitude of the external magnetic field increases
Classical lattice spin models involving singular interactions isotropic in spin space
We address here a few classical lattice spin models, involving n-component unit vectors (n=2,3), associated with a D-dimensional lattice ZD,D=1,2, and interacting via a pair potential restricted to nearest neighbors and being isotropic in spin space, i.e., defined by a function of the scalar product between the interacting spins. When the potential involves a continuous function of the scalar product, the Mermin-Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures when D=1; on the other hand, we have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to +∞ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for D=1, showing an absence of phase transitions and an absence of orientational order at all finite temperatures in the thermodynamic limit; for D=2, and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures and suggest the existence of a BerezinskiÄ-Kosterlitz-Thouless transition