Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.Comment: 21 pages, 8 figure

Condensation of vortices in the X-Y model in 3d: a disorder parameter

A disorder parameter is constructed which signals the condensation of vortices. The construction is tested by numerical simulations.Comment: 9 pages, 5 postscript figures, typset using REVTE

Exact Enumeration and Scaling for Fragmentation of Percolation Clusters

The fragmentation properties of percolation clusters yield information about their structure. Monte Carlo simulations and exact cluster enumeration for a square bond lattice and exact calculations for the Bethe lattice are used to study the fragmentation probability as(p) of clusters of mass s at an occupation probability p and the likelihood bs′s(p) that fragmentation of an s cluster will result in a daughter cluster of mass s′. Evidence is presented to support the scaling laws as(pc)∼s and bs′s(pc)=s-φg(s′/s), with φ=2-σ given by the standard cluster-number scaling exponent σ. Simulations for d=2 verify the finite-size-scaling form cs′sL(pc)=s1-φg̃(s′/s,s/Ldf) of the product cs′s(pc)=as(pc)bs′s(pc), where L is the lattice size and df is the fractal dimension. Exact calculations of the fragmentation probability fst of a cluster of mass s and perimeter t indicate that branches are important even on the maximum perimeter clusters. These calculations also show that the minimum of bs′s(p) near s′=s/2, where the two daughter masses are comparable, deepens with increasing p

Chiral perturbation theory, finite size effects and the three-dimensional XYXY model

We study finite size effects of the d=3 $XY$ model in terms of the chiral perturbation theory. We calculate by Monte Carlo simulations physical quantities which are, to order of $(1/L)^2$, uniquely determined only by two low energy constants. They are the magnetization and the helicity modulus (or the Goldstone boson decay constant) in infinite volume. We also pay a special attention to the region of the validity of the two possible expansions in the theory.Comment: 34 pages ( 9 PS files are included. harvmac and epsf macros are needed. ), KYUSHU-HET-17, SAGA-HE-6

Phase Transitions in Bilayer Heisenberg Model with General Couplings

The ground state properties and phase diagram of the bilayer square-lattice Heisenberg model are studied in a broad parameter space of intralayer exchange couplings, assuming an antiferromagnetic coupling between constituent layers. In the classical limit, the model exhibits three phases: two of these are ordered phases specified by the ordering wave vectors (pi,pi;pi) and (0,0;pi), where the third component of each indecates the antiferromagnetic orientation between layers, while another one is a canted phase, stabilized by competing interactions. The effects of quantum fluctuations in the model with S=1/2 have been explored by means of dimer mean-field theory, small-system exact diagonalization, and high-order perturbation expansions about the interlayer dimer limit.Comment: 15 pages, LaTeX, 12 figures, uses jpsj.sty, revised version: some discussion to a related model and references added, submitted to the Journal of the Physical Society of Japa

Determination of filter-cake thicknesses from on-line flow measurements and gas/particle transport modeling

The use of cylindrical candle filters to remove fine ({approx}0.005 mm) particles from hot ({approx}500- 900{degrees}C) gas streams currently is being developed for applications in advanced pressurized fluidized bed combustion (PFBC) and integrated gasification combined cycle (IGCC) technologies. Successfully deployed with hot-gas filtration, PFBC and IGCC technologies will allow the conversion of coal to electrical energy by direct passage of the filtered gases into non-ruggedized turbines and thus provide substantially greater conversion efficiencies with reduced environmental impacts. In the usual approach, one or more clusters of candle filters are suspended from a tubesheet in a pressurized (P {approx_lt}1 MPa) vessel into which hot gases and suspended particles enter, the gases pass through the walls of the cylindrical filters, and the filtered particles form a cake on the outside of each filter. The cake is then removed periodically by a backpulse of compressed air from inside the filter, which passes through the filter wall and filter cake. In various development or demonstration systems the thickness of the filter cake has proved to be an important, but unknown, process parameter. This paper describes a physical model for cake and pressure buildups between cleaning backpulses, and for longer term buildups of the ``baseline`` pressure drop, as caused by incomplete filter cleaning and/or re-entrainment. When combined with operating data and laboratory measurements of the cake porosity, the model may be used to calculate the (average) filter permeability, the filter-cake thickness and permeability, and the fraction of filter-cake left on the filter by the cleaning backpulse or re-entrained after the backpulse. When used for a variety of operating conditions (e.g., different coals, sorbents, temperatures, etc.), the model eventually may provide useful information on how the filter-cake properties depend on the various operating parameters

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.Comment: 6 pages, to appear in JPSJ 70 (2001

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.

Critical behavior of the planar magnet model in three dimensions

We use a hybrid Monte Carlo algorithm in which a single-cluster update is combined with the over-relaxation and Metropolis spin re-orientation algorithm. Periodic boundary conditions were applied in all directions. We have calculated the fourth-order cumulant in finite size lattices using the single-histogram re-weighting method. Using finite-size scaling theory, we obtained the critical temperature which is very different from that of the usual XY model. At the critical temperature, we calculated the susceptibility and the magnetization on lattices of size up to $42^3$. Using finite-size scaling theory we accurately determine the critical exponents of the model and find that $\nu$=0.670(7), $\gamma/\nu$=1.9696(37), and $\beta/\nu$=0.515(2). Thus, we conclude that the model belongs to the same universality class with the XY model, as expected.Comment: 11 pages, 5 figure

Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Pad\'e approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with $\alpha (= J_2/J_1)$. The spin-gap phase persists down to $J_3=0$ (single layer limit) for 0.45 \simleq \alpha \simleq 0.65. The crossover of the short range order within the disordered phase is also discussed.Comment: 4 pages, 6 figures, One reference adde