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

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

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.

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

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

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient

Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.Comment: 23 pages, latex, no figure

Flux Pinning and Phase Transitions in Model High-Temperature Superconductors with Columnar Defects

We calculate the degree of flux pinning by defects in model high-temperature superconductors (HTSC's). The HTSC is modeled as a three-dimensional network of resistively-shunted Josephson junctions in an external magnetic field, corresponding to a HTSC in the extreme Type-II limit. Disorder is introduced either by randomizing the coupling between grains (Model A disorder) or by removing grains (Model B disorder). Three types of defects are considered: point disorder, random line disorder, and periodic line disorder; but the emphasis is on random line disorder. Static and dynamic properties of the models are determined by Monte Carlo simulations and by solution of the analogous coupled overdamped Josephson equations in the presence of thermal noise. Random line defects considerably raise the superconducting transition temperature T$_c(B)$, and increase the apparent critical current density J$_c(B,T)$, in comparison to the defect-free crystal. They are more effective in these respects than a comparable volume density of point defects, in agreement with the experiments of Civale {\it et al}. Periodic line defects commensurate with the flux lattice are found to raise T$_c(B)$ even more than do random line defects. Random line defects are most effective when their density approximately equals the flux density. Near T$_c(B)$, our static and dynamic results appear consistent with the anisotropic Bose glass scaling hypotheses of Nelson and Vinokur, but with possibly different critical indices:Comment: 10 pages, LaTeX(REVTeX v3.0, twocolumn), 11 figures (not included