Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and Variational Methods" in Hofgeismar, Germany 201

Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

Tasks for multivariate network analysis

In Chap. 1, a multivariate network was defined as having two important characteristics. First, nodes are connected to each other via links; there is topological structure. Second, being multivariate, nodes and links have attributes associated with them, with these attributes having a value. In this chapter, we describe tasks associated with multivariate networks. We consider a task to be an activity that a user wishes to accomplish by interacting with a visual representation of a multivariate network. This implies that there is user intent [13], and that the network has been presented visually. At the highest level, this intent is usually described as the goal of obtaining insight about the data being studied [6]

Specific Heat Study on a Novel Spin-Gapped System : (CH_3)_2NH_2CuCl_3

Specific heat measurements down to 120mK have been performed on a quasi-one-dimensional $S=1/2$ spin-gapped system (CH$_3$)$_2$NH$_2$CuCl$_3$ in a magnetic field up to 8 T. This compound has a characteristic magnetization curve which shows a gapless ground state and a plateau at 1/2 of the saturation value. We have observed a spontaneous antiferromagnetic ordering and a field-induced one below and above the 1/2 plateau field range, respectively. The field versus temperature phase diagram is quite unusual and completely different from those of the other quantum spin systems investigated so far. In the plateau field range, a double-structure in the specific heat is observed, reflecting the coexistence of ferromagnetic and antiferromagnetic excitations. These behaviors are discussed on the basis of a recently proposed novel quantum spin chain model consisting of weakly coupled ferromagnetic and antiferromagnetic dimers.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp

Mixed Heisenberg Chains. I. The Ground State Problem

We consider a mechanism for competing interactions in alternating Heisenberg spin chains due to the formation of local spin-singlet pairs. The competition of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating chains.Comment: 7 pages, RevTeX, 4 embedded eps figures, final versio

Phase diagram and hidden order for generalized spin ladders

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the $S=1/2$ chain with competing nn and nnn interactions, the $S=1/2$ chain with alternating exchange and the antiferromagnetic $S=1$ chain. The Majumdar-Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the af $S=1$ chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar-Ghosh points are in the same phase as the af $S=1$ chain.Comment: 23 pages, REVTEX, 7 figure

Ground State Property of an Alternating Spin Ladder Involving Two Kinds of Inter-Chain Interactions

The ground state property of the alternating spin ladder is studied in the case that the system involves an antiferromagnetic intra-chain interaction as well as two kinds of inter-chain interactions; one is between spins of the same magnitude and the other is between spins with different magnitudes. The calculation has been carried out by the exact diagonalization method. As a consequence of the competition among interactions, the system is revealed to show an interesting variety of phases in the ground state property. Its phase diagram is exhibited in the parameter space of the system. We find that, however small the total amount of the inter-chain interactions is, the ferrimagnetic ground state becomes unstable in a certain region. In this case, which of the ferrimagnetic and the singlet ground state to appear is determined only by the ratio between the inter-chain interactions regardless of their total amount. The nature of two phases appearing in the singlet region of the phase diagram and the type of the phase transition between them are also discussed. The results are ensured by comparing with those of obtained in other models which are contained in our model as special limiting cases.Comment: 12 pages, 9 PostScript figure

Dynamical structure factors of S=1/2S=1/2 two-leg spin ladder systems

We investigate dynamical properties of $S=1/2$ two-leg spin ladder systems. In a strong coupling region, an isolated mode appears in the lowest excited states, while in a weak coupling region, an isolated mode is reduced and the lowest excited states become a lower bound of the excitation continuum. We find in the system with equal intrachain and interchain couplings that due to a cyclic four-spin interaction, the distribution of the weights for the dynamical structure factor and characteristics of the lowest excited states are strongly influenced. The dynamical properties of two systems proposed for ${\rm SrCu_2O_3}$ are also discussed.Comment: 5 pages, 6 figure

Thermodynamic properties of ferromagnetic mixed-spin chain systems

Using a combination of high-temperature series expansion, exact diagonalization and quantum Monte Carlo, we perform a complementary analysis of the thermodynamic properties of quasi-one-dimensional mixed-spin systems with alternating magnetic moments. In addition to explicit series expansions for small spin quantum numbers, we present an expansion that allows a direct evaluation of the series coefficients as a function of spin quantum numbers. Due to the presence of excitations of both acoustic and optical nature, the specific heat of a mixed-spin chain displays a double-peak-like structure, which is more pronounced for ferromagnetic than for antiferromagnetic intra-chain exchange. We link these results to an analytically solvable half-classical limit. Finally, we extend our series expansion to incorporate the single-ion anisotropies relevant for the molecular mixed-spin ferromagnetic chain material MnNi(NO$_{2}$)$_{4}$(ethylenediamine)$_{2}$, with alternating spins of magnitude 5/2 and 1. Including a weak inter-chain coupling, we show that the observed susceptibility allows for an excellent fit, and the extraction of microscopic exchange parameters.Comment: 8 pages including 7 figures, submitted to Phys. Rev. B; series extended to 29th. QMC adde

Two-magnon Raman scattering in spin-ladder geometries and the ratio of rung and leg exchange constants

We discuss ways in which the ratio of exchange constants along the rungs and legs of a spin-ladder material influences the two-magnon Raman scattering spectra and hence can be determined from it. We show that within the Fleury-Loudon-Elliott approach, the Raman line-shape does not change with polarization geometries. This lineshape is well known to be difficult to calculate accurately from theory. However, the Raman scattering intensities do vary with polarization geometries, which are easy to calculate. With some assumptions about the Raman scattering Hamiltonian, the latter can be used to estimate the ratio of exchange constants. We apply these results to Sugai's recent measurements of Raman scattering from spin-ladder materials such as La$_6$Ca$_8$Cu$_{24}$O$_{41}$ and Sr$_{14}$Cu$_{24}$O$_{41}$.Comment: 5 pages, revtex. Latest version focuses on ladder materials, with a detailed examination of the role of Heisenberg-like coupling constants which appear in the Fleury-Loudon-Elliott scattering operator but are rarely discussed in the literatur