210 research outputs found
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
Higher orders of the high-temperature expansion for the Ising model in three dimensions
The new algorithm of the finite lattice method is applied to generate the
high-temperature expansion series of the simple cubic Ising model to
for the free energy, to for the magnetic
susceptibility and to for the second moment correlation length.
The series are analyzed to give the precise value of the critical point and the
critical exponents of the model.Comment: Lattice2003(Higgs), 3 pages, 2 figure
Osculating and neighbour-avoiding polygons on the square lattice
We study two simple modifications of self-avoiding polygons. Osculating
polygons are a super-set in which we allow the perimeter of the polygon to
touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest
neighbour vertices provided these are joined by the associated edge and thus
form a sub-set of self-avoiding polygons. We use the finite lattice method to
count the number of osculating polygons and neighbour-avoiding polygons on the
square lattice. We also calculate their radius of gyration and the first
area-weighted moment. Analysis of the series confirms exact predictions for the
critical exponents and the universality of various amplitude combinations. For
both cases we have found exact solutions for the number of convex and
almost-convex polygons.Comment: 14 pages, 5 figure
Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model
We have calculated the large-q expansion for the energy cumulants and the
magnetization cumulants at the phase transition point in the two-dimensional
q-state Potts model to the 21st or 23rd order in using the finite
lattice method. The obtained series allow us to give very precise estimates of
the cumulants for on the first order transition point. The result
confirms us the correctness of the conjecture by Bhattacharya et al. on the
asymptotic behavior not only of the energy cumulants but also of the
magnetization cumulants for .Comment: 36 pages, LaTeX, 20 postscript figures, to appear in Nuclear Physics
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-
Large- expansion of the specific heat for the two-dimensional -state Potts model
We have calculated the large- expansion for the specific heat at the phase
transition point in the two-dimensional -state Potts model to the 23rd order
in using the finite lattice method. The obtained series allows us
to give highly convergent estimates of the specific heat for on the first
order transition point. The result confirm us the correctness of the conjecture
by Bhattacharya et al. on the asymptotic behavior of the specific heat for .Comment: 7 pages, LaTeX, 2 postscript figure
Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
It is shown that a recently conjectured form for the critical scaling
function for planar self-avoiding polygons weighted by their perimeter and area
also follows from an exact renormalization group flow into the branched polymer
problem, combined with the dimensional reduction arguments of Parisi and
Sourlas. The result is generalized to higher-order multicritical points,
yielding exact values for all their critical exponents and exact forms for the
associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing
theta-point results clarified, some references added/update
Series studies of the Potts model. II: Bulk series for the square lattice
The finite lattice method of series expansion has been used to extend
low-temperature series for the partition function, order parameter and
susceptibility of the -state Potts model to order (i.e. ),
, , , , , , and
for , 3, 4, \dots 9 and 10 respectively. These series are used
to test techniques designed to distinguish first-order transitions from
continuous transitions. New numerical values are also obtained for the
-state Potts model with .Comment: 32 pages, incl. 3 figures, incl. 3 figure
Perimeter Generating Functions For The Mean-Squared Radius Of Gyration Of Convex Polygons
We have derived long series expansions for the perimeter generating functions
of the radius of gyration of various polygons with a convexity constraint.
Using the series we numerically find simple (algebraic) exact solutions for the
generating functions. In all cases the size exponent .Comment: 8 pages, 1 figur
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
- …