Nishimori point in the 2D +/- J random-bond Ising model

We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free-energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p_c = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.Comment: 4 pages REVTeX, 3 PostScript figures; final version to appear in Phys. Rev. Lett.; several small changes and extended explanation

Laboratory Measurement of the Pure Rotational Transitions of the HCNH+ and its Isotopic Species

The pure rotational transitions of the protonated hydrogen cyanide ion, HCNH+, and its isotopic species, HCND+ and DCND+, were measured in the 107 - 482 GHz region with a source modulated microwave spectrometer. The ions were generated in the cell with a magnetically confined dc-glow discharge of HCN and/or DCN. The rotational constant B0 and the centrifugal distortion constant D0 for each ion were precisely determined by a least-squares fitting to the observed spectral lines. The observed rotational transition frequencies by laboratory spectroscopy and the predicted ones are accurate in about 30 to 40 kHz and are useful as rest frequencies for astronomical searches of HCNH+ and HCND+.Comment: 14 pages in TeX, 1 figures in JPE

Nishimori point in random-bond Ising and Potts models in 2D

We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3Comment: 11 pages, 3 figures. Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200

A 2k2k-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$

The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte

Monoiodoacetic acid induces arthritis and synovitis in rats in a dose- and time-dependent manner: proposed model-specific scoring systems

SummaryObjectiveIn a rat monoiodoacetic acid (MIA)-induced arthritis model, the amount of MIA commonly used was too high, resulting in rapid bone destruction. We examined the effect of MIA concentrations on articular cartilage and infrapatellar fat pad (IFP). We also established an original system for “macroscopic cartilage and bone score” and “IFP inflammation score” specific to the rat MIA-induced arthritis model.DesignMale Wistar rats received a single intra-articular injection of MIA in the knee. The amount of MIA was 0.1, 0.2, 0.5, and 1 mg respectively. Articular cartilage was evaluated at 2–12 weeks. IFP was also observed at 3–14 days.ResultsMacroscopically, low MIA doses induced punctate depressions on the cartilage surface, and cartilage erosion proceeded slowly over 12 weeks, while higher MIA doses already induced cartilage erosion at 2 weeks, followed by bone destruction. MIA macroscopic cartilage and bone score, OARSI histological score, and Mankin score increased in a dose- and time-dependent manner. The IFP inflammation score peaked at 5 days in low dose groups, then decreased, while in high dose groups, the IFP score continued to increase over 14 days due to IFP fibrosis.ConclusionsPunctate depressions, cartilage erosion, and bone destruction were observed in the MIA-induced arthritis model. The macroscopic cartilage and bone scoring enabled the quantification of cartilage degeneration and demonstrated that MIA-induced arthritis progressed in a dose- and time-dependent manner. IFP inflammation scores revealed that 0.2 mg MIA induced reversible synovitis, while 1 mg MIA induced fibrosis of the IFP body

Numerical Study of Competing Spin-Glass and Ferromagnetic Order

Two and three dimensional random Ising models with a Gaussian distribution of couplings with variance $J$ and non-vanishing mean value $J_0$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the ($J_0,J$) plane after rescaling can be collapsed on two curves: one for $J_0/J > r_c$ and other for $J_0/J < r_c$. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions respectively. No evidence for an extra phase is found.Comment: a bit more data is taken, 5 pages, 4 eps figures included, to appear in PR

Duality and Multicritical Point of Two-Dimensional Spin Glasses

Determination of the precise location of the multicritical point and phase boundary is a target of active current research in the theory of spin glasses. In this short note we develop a duality argument to predict the location of the multicritical point and the shape of the phase boundary in models of spin glasses on the square lattice.Comment: 4 pages, 1 figure; Reference updated, definition of \tilde{V} added; to be published in J. Phys. Soc. Jp

Duality in finite-dimensional spin glasses

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.Comment: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phy

Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions

An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under the replica boundary condition. Our values of the critical temperature and exponent, obtained by finite-size scaling, are in good agreement with those of the standard MC and the series expansion studies. In addition, two exponents, the stiffness exponent and the fractal dimension of the domain wall, which characterize the ordered phase, are obtained. The latter value is larger than d-1, indicating that the domain wall is really rough in the 4d Ising spin glass phase.Comment: 9 pages Latex(Revtex), 8 eps figure