74 research outputs found

    New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

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    We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter

    Correlations and Binding in 4D Dynamical Triangulation

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    We study correlations on the euclidean spacetimes generated in Monte Carlo simulations of the model. In the elongated phase, curvature correlations appear to fall off like a fractional power. Near the transition to the crumpled phase this power is consistent with 4. We also present improved data of our computations of the binding energy of test particles.Comment: 4 pages for proceedings Lattice '95; latex, espcrc2.sty and postscript figure files packed with uufiles; corrected packing, contents of paper unchange

    Specific Heat Exponent for the 3-d Ising Model from a 24-th Order High Temperature Series

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    We compute high temperature expansions of the 3-d Ising model using a recursive transfer-matrix algorithm and extend the expansion of the free energy to 24th order. Using ID-Pade and ratio methods, we extract the critical exponent of the specific heat to be alpha=0.104(4).Comment: 10 pages, LaTeX with 5 eps-figures using epsf.sty, IASSNS-93/83 and WUB-93-4

    Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet

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    Various series expansions have been developed for the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T=0, Ising expansions are used to study the properties of the N\'{e}el-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be (J2/J1)c=2.537(5)(J_2/J_1)_c=2.537(5). Quantities computed include the staggered magnetization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimates that the ratio of the intra- and inter-layer exchange constants to be J2/J10.07J_2/J_1\simeq 0.07 for cuprate superconductor YBa2Cu3O6.2YBa_2Cu_3O_{6.2}.Comment: RevTeX, 9 figure

    Scaling of loop-erased walks in 2 to 4 dimensions

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    We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2,3, and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in d=4d=4, simulations in lower dimensions were done for completeness and in order to test the algorithm. In d=2d=2, we verify with high precision the prediction D=5/4D=5/4, where the number of steps nn after erasure scales with the number NN of steps before erasure as nND/2n\sim N^{D/2}. In d=3d=3 we again find a power law, but with an exponent different from the one found in the most precise previous simulations: D=1.6236±0.0004D = 1.6236\pm 0.0004. Finally, we see clear deviations from the naive scaling nNn\sim N in d=4d=4. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect.Comment: 3 pages, including 3 figure

    Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

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    We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic 2×122\times 12 ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is λc0.8\lambda_c\simeq 0.8, with λ\lambda defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of λc1.25\lambda_c\simeq 1.25. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic (λ=1)(\lambda=1) spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure

    High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

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    We determine the critical exponents for the XY universality class in three dimensions, which is expected to describe the λ\lambda-transition in 4{}^4He. They are obtained from the analysis of high-temperature series computed for a two-component λϕ4\lambda\phi^4 model. The parameter λ\lambda is fixed such that the leading corrections to scaling vanish. We obtain ν=0.67166(55)\nu = 0.67166(55), γ=1.3179(11)\gamma = 1.3179(11), α=0.0150(17)\alpha=-0.0150(17). These estimates improve previous theoretical determinations and agree with the more precise experimental results for liquid Helium.Comment: 8 pages, revte

    Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

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    Using a renormalized linked-cluster-expansion method, we have extended to order β23\beta^{23} the high-temperature series for the susceptibility χ\chi and the second-moment correlation length ξ\xi of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of χ\chi and ξ\xi. Our best estimates for the inverse critical temperatures are βcsc=0.221654(1)\beta^{sc}_c=0.221654(1) and βcbcc=0.1573725(6)\beta^{bcc}_c=0.1573725(6). For the susceptibility exponent we get γ=1.2375(6)\gamma=1.2375(6) and for the correlation length exponent we get ν=0.6302(4)\nu=0.6302(4). The ratio of the critical amplitudes of χ\chi above and below the critical temperature is estimated to be C+/C=4.762(8)C_+/C_-=4.762(8). The analogous ratio for ξ\xi is estimated to be f+/f=1.963(8)f_+/f_-=1.963(8). For the correction-to-scaling amplitude ratio we obtain aξ+/aχ+=0.87(6)a^+_{\xi}/a^+_{\chi}=0.87(6).Comment: Misprints corrected, 8 pages, latex, no figure

    Studies of Quantum Spin Ladders at T=0 and at High Temperatures by Series Expansions

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    We have carried out extensive series studies, at T=0 and at high temperatures, of 2-chain and 3-chain spin-half ladder systems with antiferromagnetic intrachain and both antiferromagnetic and ferromagnetic interchain couplings. Our results confirm the existence of a gap in the 2-chain Heisenberg ladders for all non-zero values of the interchain couplings. Complete dispersion relations for the spin-wave excitations are computed. For 3-chain systems, our results are consistent with a gapless spectrum. We also calculate the uniform magnetic susceptibility and specific heat as a function of temperature. We find that as T0T\to 0, for the 2-chain system the uniform susceptibility goes rapidly to zero, whereas for the 3-chain system it approaches a finite value. These results are compared in detail with previous studies of finite systems.Comment: RevTeX, 14 figure