153 research outputs found
Yet another way to obtain low temperature expansions for discrete spin systems
I present a modification of the shadow-lattice technique, which allows one to
derive low temperature series for discrete spin models to high orders. Results
are given for the 3-d Ising model up to 64 excited bonds, for the 4-d Ising
model up to 96 excited bonds and the 3-d Potts model up to 56 excited bonds.Comment: 7 pages, DESY 92-16
Monte Carlo calculation for systems consisting of several coordinate patches
I investigate the time step dependence of Monte Carlo simulations for
coordinate-spaces consisting of several patches. It is shown that a naive
kinetic term does not necessarily converge to the same spectrum as a
Hamiltonian calculation. Then an improved kinetic term is presented which
allows one to connect the Monte Carlo and Rayleigh-Ritz results of intermediate
volume SU(2) gauge theory.Comment: 18 page
The 4d one component lattice model in the broken phase revisited
Measurements of various physical quantities in the symmetry broken phase of
the one component lattice with standard action, are shown to be
consistent with the critical behavior obtained by renormalization group
analyses. This is in contrast to recent conclusions by another group, who
further claim that the unconventional scaling behavior they observe, when
extended to the complete Higgs sector of the Standard Model, would alter the
conventional triviality bound on the mass of the Higgs.Comment: 15 pages, 3 figure
Low-Temperature Series for Ising Model by Finite-Lattice Method
We have calculated the low-temperature series for the second moment of the
correlation function in Ising model to order and for the free
energy of Absolute Value Solid-on-Solid (ASOS) model to order , using
the finite-lattice method.Comment: 3pages, latex, no figures, talk given at LATTICE'94, to appear in the
proceeding
Low-Temperature Series for the Correlation Length in Ising Model
We extend low-temperature series for the second moment of the correlation
function in simple-cubic Ising model from to using
finite-lattice method, and combining with the series for the susceptibility we
obtain the low-temperature series for the second-moment correlation length to
. An analysis of the obtained series by inhomogeneous differential
approximants gives critical exponents and .Comment: 13 pages + 5 uuencoded epsf figures in Latex, OPCT-94-
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
Series expansions without diagrams
We discuss the use of recursive enumeration schemes to obtain low and high
temperature series expansions for discrete statistical systems. Using linear
combinations of generalized helical lattices, the method is competitive with
diagramatic approaches and is easily generalizable. We illustrate the approach
using the Ising model and generate low temperature series in up to five
dimensions and high temperature series in three dimensions. The method is
general and can be applied to any discrete model. We describe how it would work
for Potts models.Comment: 24 pages, IASSNS-HEP-93/1
Comparison of Monte Carlo Results for the 3D Ising Interface Tension and Interface Energy with (Extrapolated) Series Expansions
We compare Monte Carlo results for the interface tension and interface energy
of the 3-dimensional Ising model with Pad\'e and inhomogeneous differential
approximants of the low temperature series that was recently extended by Arisue
to order in . The series is expected to suffer
from the roughening singularity at . The comparison with the
Monte Carlo data shows that the Pad\'e and inhomogeneous differential
approximants fail to improve the truncated series result of the interface
tension and the interface energy in the region around the roughening
transition. The Monte Carlo data show that the specific heat displays a peak in
the smooth phase. Neither the truncated series nor the Pad\'e approximants find
this peak. We also compare Monte Carlo data for the energy of the ASOS model
with the corresponding low temperature series that we extended to order
.Comment: 22 pages, 9 figures appended as 3 PS-files, preprints
CERN-TH.7029/93, MS-TPI-93-0
Low-temperature effective potential of the Ising model
We study the low-temperature effective potential of the Ising model. We
evaluate the three-point and four-point zero-momentum renormalized coupling
constants that parametrize the expansion of the effective potential near the
coexistence curve. These results are obtained by a constrained analysis of the
-expansion that uses accurate estimates for the two-dimensional Ising
model.Comment: 16 pages, RevTex, few minor change
A Magnetic Monopole in Pure SU(2) Gauge Theory
The magnetic monopole in euclidean pure SU(2) gauge theory is investigated
using a background field method on the lattice.
With Monte Carlo methods we study the mass of the monopole in the full
quantum theory.
The monopole background under the quantum fluctuations is induced by imposing
fixed monopole boundary conditions on the walls of a finite lattice volume.
By varying the gauge coupling it is possible to study monopoles with scales
from the hadronic scale up to high energies.
The results for the monopole mass are consistent with a conjecture we made
previously in a realization of the dual superconductor hypothesis of
confinement.Comment: 33 pages uufiles-compressed PostScript including (all) 12 figures,
preprint numbers ITFA-93-19 (Amsterdam), OUTP-93-21P (Oxford), DFTUZ/93/23
(Zaragoza
- …