Orbital order in classical models of transition-metal compounds

We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these models exhibit a long-range order which arises via an "order by disorder" mechanism. This strongly indicates that there is orbital ordering in the quantum version of these models, notwithstanding recent rigorous results on the absence of spin order in these systems.Comment: 7 pages, 1 eps fi

Colligative properties of solutions: II. Vanishing concentrations

We continue our study of colligative properties of solutions initiated in math-ph/0407034. We focus on the situations where, in a system of linear size $L$, the concentration and the chemical potential scale like $c=\xi/L$ and $h=b/L$, respectively. We find that there exists a critical value \xit such that no phase separation occurs for \xi\le\xit while, for \xi>\xit, the two phases of the solvent coexist for an interval of values of $b$. Moreover, phase separation begins abruptly in the sense that a macroscopic fraction of the system suddenly freezes (or melts) forming a crystal (or droplet) of the complementary phase when $b$ reaches a critical value. For certain values of system parameters, under ``frozen'' boundary conditions, phase separation also ends abruptly in the sense that the equilibrium droplet grows continuously with increasing $b$ and then suddenly jumps in size to subsume the entire system. Our findings indicate that the onset of freezing-point depression is in fact a surface phenomenon.Comment: 27 pages, 1 fig; see also math-ph/0407034 (both to appear in JSP

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Colligative properties of solutions: I. Fixed concentrations

Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing point depression. The limit of infinitesimal concentrations is described in a subsequent paper.Comment: 28 pages, 1 fig; see also math-ph/0407035 (both to appear in JSP

The topographical anatomy of the round window and related structures for the purpose of cochlear implant surgery

The treatment of total deafness using a cochlear implant has now become a routine medical procedure. The tendency to expand the audiological indications for cochlear stimulation and to preserve the remnants of hearing has brought new problems. The authors have studied the topographical anatomy of the internal structures of the ear in the area where cochleostomy is usually performed and an implant electrode inserted. Ten human temporal bones were obtained from cadavers and prepared in a formalin stain. After dissection of the bone in the area of round and oval windows, the following diameters were measured using a microscope with a scale: the transverse diameters of the cochlear and vestibular scalae at the level of the centre of the round window and 0.5 mm anteriorly to the round window, the distance between the windows and the distances from the end of the spiral lamina to the centre of the round window and to its anterior margin. The width of the cochlear scala at the level of the round window was 1.23 mm, and 0.5 mm anteriorly to the round window membrane it was 1.24 mm. The corresponding diameters for the vestibular scala are 1.34 and 1.27 mm. The distances from the end of the spiral lamina to the centre of the round window and to its anterior margin are 1.26 and 2.06 respectively. The authors noted that the two methods of electrode insertion show a difference of 2 mm in the length of the stimulated spiral lamina. The average total length of the unstimulated lamina is 2.06 and 4.06 in the two situations respectively

On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Let

Multiferroic behavior in the new double-perovskite Lu2_2MnCoO6_6

We present a new member of the multiferroic oxides, Lu$_2$MnCoO$_6$, which we have investigated using X-ray diffraction, neutron diffraction, specific heat, magnetization, electric polarization, and dielectric constant measurements. This material possesses an electric polarization strongly coupled to a net magnetization below 35 K, despite the antiferromagnetic ordering of the $S = 3/2$ Mn$^{4+}$ and Co$^{2+}$ spins in an $\uparrow \uparrow \downarrow \downarrow$ configuration along the c-direction. We discuss the magnetic order in terms of a condensation of domain boundaries between $\uparrow \uparrow$ and $\downarrow \downarrow$ ferromagnetic domains, with each domain boundary producing a net electric polarization due to spatial inversion symmetry breaking. In an applied magnetic field the domain boundaries slide, controlling the size of the net magnetization, electric polarization, and magnetoelectric coupling

Pulsed laser deposition growth of heteroepitaxial YBa2Cu3O7/La0.67Ca0.33MnO3 superlattices on NdGaO3 and Sr0.7La0.3Al0.65Ta0.35O3 substrates

Heteroepitaxial superlattices of [YBa2Cu3O7(n)/ La0.67Ca0.33MnO3(m)]x, where n and m are the number of YBCO and LCMO monolayers and x the number of bilayer repetitions, have been grown with pulsed laser deposition on NdGaO3 (110) and Sr0.7La0.3Al0.65Ta0.35O3 (LSAT) (001). These substrates are well lattice matched with YBCO and LCMO and, unlike the commonly used SrTiO3, they do not give rise to complex and uncontrolled strain effects due to structural transitions at low temperature. The growth dynamics and the structure have been studied in-situ with reflection high energy electron diffraction (RHEED) and ex-situ with scanning transmission electron microscopy (STEM), x-ray diffraction, and neutron reflectometry. The individual layers are found to be flat and continuous over long lateral distances with sharp and coherent interfaces and with a well-defined thickness of the individual layer. The only visible defects are antiphase boundaries in the YBCO layers that originate from perovskite unit cell height steps at the interfaces with the LCMO layers. We also find that the first YBCO monolayer at the interface with LCMO has an unusual growth dynamics and is lacking the CuO chain layer while the subsequent YBCO layers have the regular Y-123 structure. Accordingly, the CuO2 bilayers at both the LCMO/YBCO and the YBCO/LCMO interfaces are lacking one of their neighboring CuO chain layers and thus half of their hole doping reservoir. Nevertheless, from electric transport measurements on asuperlattice with n=2 we obtain evidence that the interfacial CuO2 bilayers remain conducting and even exhibit the onset of a superconducting transition at very low temperature. Finally, we show from dc magnetization and neutron reflectometry measurements that the LCMO layers are strongly ferromagnetic

A numerical approach to copolymers at selective interfaces

We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known. In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include: - Various numerical observations that suggest that the critical line lies strictly in between the two bounds. - A rigorous statistical test based on concentration inequalities and super-additivity, for determining whether a given point of the phase diagram is in the localized phase. This is applied in particular to show that, with a very low level of error, the lower bound does not coincide with the critical line. - An analysis of the precise asymptotic behavior of the partition function in the delocalized phase, with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a Brownian scaling. - A new proof of the lower bound on the critical line. This proof relies on a characterization of the localized regime which is more appealing for interpreting the numerical data.Comment: accepted for publication on J. Stat. Phy