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To obtain an unusually large set of exact solutions for even-number localized correlations of the standard square Ising model, a method is developed that combines traditional Pfaffian techniques with linear-algebraic systems of correlation identities having interaction-dependent coefficients.Two eight-site clusters (subclusters of the "Greek cross" cluster) are studied, and altogether sixty different even-number correlations are determined exactly at all temperatures. Besides demonstrating the existence of degeneracies within the set of exact solutions, the solution curve for an eight-site correlation is evidently the first of such large order to be displayed for an Ising model on any regular planar lattice. Significant time as well as labor efficiency of the method is clearly demonstrated since relatively few correlations need to be actually calculated by Pfaffian techniques in order to obtain large additional numbers of multisite correlation solutions using much simpler linear-algebraic procedures.

The authors describe a signal distribution network (SDN) for quantum-dot cellular automata (QCA) devices. This network allows the distribution of a set of N inputs to an arbitrary number of combinational functions, overcoming the challenges associated with wire crossings that have faced QCA systems for many years. As an additional benefit, the proposed SDN requires only four distinct clock signals, regardless of the number of inputs or outputs, and those clock signals each repeat a very simple pattern. Furthermore, this network is highly scalable, completing the distribution of N inputs to an arbitrary number of distributed signals and an arbitrary number of outputs in 4N -2 clock cycles. To illustrate its operation, the authors apply the SDN to a two-input/one-output exclusive OR operation, a three-input/twooutput full adder, and a four-input/four-output multiplier.Index Terms-Nanoelectronics, quantum-dot cellular automata (QCA), quasi-adiabatic switching, wire crossing.

In production, it is common to deal with short production runs, where flexibility is required in the built-up of parts to produce numerous variants of manufactured goods. Monitoring the multivariate coefficient of variation (MCV) is an effective method to monitor the relative multivariate variability compared with the mean. Monitoring the relative multivariate variability is important when practitioners are not interested in the changes in the mean vector or the covariance matrix. Monitoring the univariate coefficient of variation in short production runs has already been successfully executed. In this paper, the statistical performance of one-sided charts for monitoring the MCV of a multivariate process with finite horizon is investigated. Prior to this work, no attempt has been made to study process monitoring of MCV in short production runs. Investigations are made when the exact shift size can be specified and when there is a random shift size. It is found that the proposed upward chart detects an increasing shift in the MCV quicker than its downward counterpart detects a decreasing shift, for the same shift size (from the nominal value). An example is presented to illustrate the implementation of the new method.

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

We present a study of the joint influence of temperature and fabrication defects on the operation of quantum-dot cellular automata (QCA) devices. Canonical ensemble, a Hubbard-type Hamiltonian and the inter-cellular Hartree approximation were used, and a statistical model has been introduced to simulate defects in the QCA devices. Parameters such as success rate and breakdown displacement factor (BDF) were defined and calculated numerically. Results show the thermal dependence of BDF values of the QCA devices. The BDF values decrease with temperature. The joint influence of randomly missing dots and temperature was also studied.