Lattice model theory of the equation of state covering the gas, liquid, and solid phases

The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon

Critical phase of a magnetic hard hexagon model on triangular lattice

We introduce a magnetic hard hexagon model with two-body restrictions for configurations of hard hexagons and investigate its critical behavior by using Monte Carlo simulations and a finite size scaling method for discreate values of activity. It turns out that the restrictions bring about a critical phase which the usual hard hexagon model does not have. An upper and a lower critical value of the discrete activity for the critical phase of the newly proposed model are estimated as 4 and 6, respectively.Comment: 11 pages, 8 Postscript figures, uses revtex.st

Naive mean field approximation for image restoration

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which is equivalent to a finite-temperature decoding method. Since a lot of computational time is needed for the MPM estimate to calculate the thermal averages, the mean field method, which is a deterministic algorithm, is often utilized to avoid this difficulty. We present a statistical-mechanical analysis of naive mean field approximation in the framework of image restoration. We compare our theoretical results with those of computer simulation, and investigate the potential of naive mean field approximation.Comment: 9 pages, 11 figure

Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulas which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices. The examples include the +-J and Gaussian Ising spin glasses on the square, hexagonal and triangular lattices, the Potts and Z_q models with chiral randomness on these lattices, and the three-dimensional +-J Ising spin glass and the random plaquette gauge model.Comment: 27 pages, 3 figure

A Spin - 3/2 Ising Model on a Square Lattice

The spin - 3/2 Ising model on a square lattice is investigated. It is shown that this model is reducible to an eight - vertex model on a surface in the parameter space spanned by coupling constants J, K, L and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space.Comment: LaTeX, 7 pages, 1 figure upon request; JETP Letters, in pres

Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice

We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis anisotropy on the triangular lattice. Both the free energy cost for long wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure

Calcium scoring using 64-slice MDCT, dual source CT and EBT: a comparative phantom study

Purpose Assessment of calcium scoring (Ca-scoring) on a 64-slice multi-detector computed tomography (MDCT) scanner, a dual-source computed tomography (DSCT) scanner and an electron beam tomography (EBT) scanner with a moving cardiac phantom as a function of heart rate, slice thickness and calcium density. Methods and materials Three artificial arteries with inserted calcifications of different sizes and densities were scanned at rest (0 beats per minute) and at 50–110 beats per minute (bpm) with an interval of 10 bpm using 64-slice MDCT, DSCT and EBT. Images were reconstructed with a slice thickness of 0.6 and 3.0 mm. Agatston score, volume score and equivalent mass score were determined for each artery. A cardiac motion susceptibility (CMS) index was introduced to assess the susceptibility of Ca-scoring to heart rate. In addition, a difference (Δ) index was introduced to assess the difference of absolute Ca-scoring on MDCT and DSCT with EBT. Results Ca-score is relatively constant up to 60 bpm and starts to decrease or increase above 70 bpm, depending on scoring method, calcification density and slice thickness. EBT showed the least susceptibility to cardiac motion with the smallest average CMS-index (2.5). The average CMS-index of 64-slice MDCT (9.0) is approximately 2.5 times the average CMS-index of DSCT (3.6). The use of a smaller slice thickness decreases the CMS-index for both CT-modalities. The Δ-index for DSCT at 0.6 mm (53.2) is approximately 30% lower than the Δ-index for 64-slice MDCT at 0.6 mm (72.0). The Δ-indexes at 3.0 mm are approximately equal for both modalities (96.9 and 102.0 for 64-slice MDCT and DSCT respectively). Conclusion Ca-scoring is influenced by heart rate, slice thickness and modality used. Ca-scoring on DSCT is approximately 50% less susceptible to cardiac motion as 64-slice MDCT. DSCT offers a better approximation of absolute calcium score on EBT than 64-slice MDCT when using a smaller slice thickness. A smaller slice thickness reduces the susceptibility to cardiac motion and reduces the difference between CT-data and EBT-data. The best approximation of EBT on CT is found for DSCT with a slice thickness of 0.6 mm

Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-cComment: RevTeX style, 20 pages, 12 figure