Magnetic Properties of a Quantum Ferrimagnet: NiCu(pba)(D_2O)_3 . 2D_2O

We report the results of magnetic measurements on a powder sample of NiCu(pba)(D_2O)_3 \cdot 2D_2O$(pba=1,3-propylenebis(oxamato)) which is one of the prototypical examples of an$S$=1/2 and 1 ferrimagnetic chain. Susceptibility($\chi$) shows a monotonous increase with decreasing temperature (T) and reaches a maximum at about 7 K. In the plot of$\chi T$versus$T$, the experimental data exhibit a broad minimum and are fit to the$\chi T$curve calculated for the ferrimagnetic Heisenberg chain composed of S=1/2 and 1. From this fit, we have evaluated the nearest-neighbor exchange constant$J/k_B=121 K$, the g-values of Ni$^{2+}$and Cu$^{2+}$,$g_{Ni}$=2.22 and$g_{Cu}$=2.09, respectively. Applied external field dependence of$\chi T$ at low temperatures is reproduced fairly well by the calculation for the same ferrimagnetic model.Comment: 7pages, 4 postscript figures, usues REVTEX. appear in J. Phys. Soc. Jpn vol 67 No.7 (1998

The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation

We have adjusted the Density Matrix Renormalization method to handle two dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground state wave function. Combining the results obtained for system sizes up-to $30 \times 6$ and finite size scaling, we derive the phase transition point and the critical exponent for the gap in the Ising model in a Transverse Field on a two dimensional square lattice.Comment: 9 pages, 8 figure

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Classical Correlation-Length Exponent in Non-Universal Quantum Phase Transition of Diluted Heisenberg Antiferromagnet

Critical behavior of the quantum phase transition of a site-diluted Heisenberg antiferromagnet on a square lattice is investigated by means of the quantum Monte Carlo simulation with the continuous-imaginary-time loop algorithm. Although the staggered spin correlation function decays in a power law with the exponent definitely depending on the spin size $S$, the correlation-length exponent is classical, i.e., $\nu=4/3$. This implies that the length scale characterizing the non-universal quantum phase transition is nothing but the mean size of connected spin clusters.Comment: 4 pages, 3 figure

An Eight-Week Trial Investigating the Efficacy and Tolerability of Atorvastatin for Children and Adolescents With Heterozygous Familial Hypercholesterolemia

This study aimed to assess the efficacy and tolerability of atorvastatin in Tanner stage (TS) 1 patients ages 6 to 10 years and TS ≥2 patients ages 10 to <18 years with genetically confirmed heterozygous familial hypercholesterolemia (HeFH) and a low density lipoprotein cholesterol (LDL-C) level of 4 mmol/l (155 mg/dl) or higher. In this open-label, 8-week study, 15 TS 1 children were treated initially with atorvastatin 5 mg/day and 24 TS ≥2 children with 10 mg/day. Doses were doubled at week 4 if the LDL-C target (<3.35 mmol/l [130 mg/dl]) was not achieved. The efficacy variables were the percentage change from baseline in LDL-C, total cholesterol (TC), triglycerides (TG), high density lipoprotein cholesterol (HDL-C), very low density lipoprotein cholesterol (VLDL-C), and apolipoprotein (Apo) A-I and Apo B. Safety evaluations included clinical monitoring, subject-reported adverse events (AEs), vital signs, and clinical laboratory tests. The mean values for LDL-C, TC, VLDL-C, and Apo B decreased by week 2 among all TS 1 and TS ≥2 patients, whereas TG, HDL-C, and Apo A-I varied considerably from week to week. After 8 weeks, the mean reduction in LDL-C was −40.7% ± 8.4 for the TS 1 children and −39.7% ± 10.3 for the TS ≥2 children. For the TS 1 patients, the mean reductions were −34.1% ± 6.9 for TC and −6.0% ± 32.1 for TG. The corresponding changes for the TS ≥2 patients were −35.6% ± 9.5 for TC and −21.1% ± 29.7 for TG. Four patients experienced mild to moderate treatment-related AEs. No serious AEs or discontinuations were reported. Overall, no difference in safety or tolerability was observed between the younger and older cohorts. Across the range of exposures after atorvastatin 5 to 10 mg (TS 1) or atorvastatin 10 to 20 mg (TS ≥2) doses for 8 weeks, clinically meaningful reductions in LDL-C, TC, VLDL-C, and Apo were observed with atorvastatin in pediatric patients who had HeFH. Atorvastatin also was well tolerated in this population

A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets

We give a sharpening of a recent result of Aschenbrenner and Pong about the maximal order type of the term ordering on the finite multisets over a wpo. Moreover we discuss an approach to compute maximal order types of well-partial orders which are related to tree embeddings

Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.Comment: RevTeX, 4 pages including 5 EPS figure

The Heisenberg model on the 1/5-depleted square lattice and the CaV4O9 compound

We investigate the ground state structure of the Heisenberg model on the 1/5-depleted square lattice for arbitrary values of the first- and second-neighbor exchange couplings. By using a mean-field Schwinger-boson approach we present a unified description of the rich ground-state diagram, which include the plaquette and dimer resonant-valence-bond phases, an incommensurate phase and other magnetic orders with complex magnetic unit cells. We also discuss some implications of ours results for the experimental realization of this model in the CaV4O9 compound.Comment: 4 pages, Latex, 7 figures included as eps file

Phase Diagram of the Spin-Orbital model on the Square Lattice

We study the phase diagram of the spin-orbital model in both the weak and strong limits of the quartic spin-orbital exchange interaction. This allows us to study quantum phase transitions in the model and to approach from both sides the most interesting intermediate-coupling regime and in particular the SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al [Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of the system is a plaquette spin-orbital liquid. We argue that the state is more complex. There is plaquette order, but it is anisotropic: bonds in one direction are stronger than those in the perpendicular direction. This order is somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg spin model.Comment: 8 pages, 4 Postscript figure