74 research outputs found

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

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

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

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

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 $(J_2/J_1)_c=2.537(5)$. 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 $J_2/J_1\simeq
0.07$ for cuprate superconductor $YBa_2Cu_3O_{6.2}$.Comment: RevTeX, 9 figure

### Scaling of loop-erased walks in 2 to 4 dimensions

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
$d=4$, simulations in lower dimensions were done for completeness and in order
to test the algorithm. In $d=2$, we verify with high precision the prediction
$D=5/4$, where the number of steps $n$ after erasure scales with the number $N$
of steps before erasure as $n\sim N^{D/2}$. In $d=3$ we again find a power law,
but with an exponent different from the one found in the most precise previous
simulations: $D = 1.6236\pm 0.0004$. Finally, we see clear deviations from the
naive scaling $n\sim N$ in $d=4$. 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

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 $2\times 12$ 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 $\lambda_c\simeq 0.8$, with $\lambda$ 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
$\lambda_c\simeq 1.25$. 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 $(\lambda=1)$ 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

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

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

Using a renormalized linked-cluster-expansion method, we have extended to
order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$
and the second-moment correlation length $\xi$ 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 $\chi$ and $\xi$. Our best
estimates for the inverse critical temperatures are
$\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the
susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation
length exponent we get $\nu=0.6302(4)$.
The ratio of the critical amplitudes of $\chi$ above and below the critical
temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for
$\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling
amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

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

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 $T\to 0$, 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

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