Thermomagnetic properties of very heavy fermions suitable for adiabatic demagnetisation refrigeration at low temperature

ABSTRACT

With the aim to improve the performance of classical paramagnetic salts for adiabatic refrigeration processes at the sub-Kelvin range, relevant thermodynamic parameters of some new Yb-based intermetallic compounds are analysed and compared. Two main applications are considered: (i) those requiring temperature fixed-points to be reached applying magnetic fields of moderate intensity for satellite applications, and (ii) those which can be used for controlled thermal drifts in laboratory applications. Different thermomagnetic trajectories of the entropy are identified depending on respective specific heat behaviours and the constraints imposed by the Nernst postulate at the sub-Kelvin range. Some simple relationships are proposed to compare the diverse magnetocaloric characteristics of different systems. This procedure allows to include the classical Cerium-Magnesium-Nitride (CMN) salt in that comparison.     

Sedimentation of homogeneous suspensions in finite vessels

The question of a possible container shape dependence of the sedimentation velocity in a homogeneous suspension is reexamined. To this end we develop a statistical theory of suspensions based on low-Reynolds-number hydrodynamics of spherical particles in a container. It is shown, to first order in the volume fraction, that in an arbitrary vessel the relative sedimentation velocity is shape independent, but that at the same time shape-dependent convection occurs. The theory forms a bridge between earlier calculations for special geometries by Beenakker and Mazur and a phenomenological theory recently proposed by Nozières.This paper is dedicated to N. G. van Kampen.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Relationship between the 2-body Parameters of the Biswas-Hamann and the Bauer-Maysenholder-Seeger Potential Functions

A theoretical relation between the Bauer-Maysenholder-Seeger (BMS) and the Biswas-Hamann (BH) potential function has been developed herein for the case of 2-body interaction. By equating derivatives of these two potential functions for the 2-body part, a loose form of BMS is expressed in terms of BH parameters with a scaling factor. The validity of the developed parametric relationships has been graphically demonstrated, and the suitability discussed with reference to the extent and direction of bond distortion.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

Symmetries of the electrodynamic interactions between chiral molecules

A quantum electrodynamics calculation of the dynamic microscopic interactions between molecules beyond the electric dipole approximation is presented. The symmetry of the resulting terms is examined with respect to rotations, parity and index permutations. Their relative importance is also considered in the short-distance limit. A dominant term which exists only in chiral molecules and which involves the coupling of the anisotropic parts of the molecular optical activities is evidenced. Associated with the coupling of the anisotropic parts of the molecular polarisabilities which is usually invoked to account for the isotropic–nematic phase transition of liquid crystals, that term accounts for the possibility of the helical order which is observed in chiral nematics (cholesterics). Introducing in addition both the short-range correlations due to the exclusion principle driven repulsive forces and the thermally-induced effect of the static multipole interactions can explain the temperature dependence of the helical pitch. No assumption will be made on the shape of the molecules.     

Mean field and the confined single homopolymer

We develop a statistical model for a confined homopolymeric chain molecule based on a monomer grand ensemble representation. The molecule is subject to a confining external field, a backbone interaction, and an attractive interaction between any pair of monomers. An exact minimum principle for the thermodynamics of the backbone in an external field is obtained, and a controlled mean field approximation results in a modified minimum principle from which relevant physical quantities such as monomer density can be found. We explore the limit in which the chain is subject to tight confinement, and make a preliminary investigation of a prototypical system.