1,217 research outputs found
Critical parameters of N-vector spin models on 3d lattices from 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 denoted as the
O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear
sigma model] have been extended to order beta^{21} on the simple cubic and the
body centered cubic lattices, for arbitrary N. The series for the second field
derivative of the susceptibility has been extended to order beta^{17}. An
analysis of the newly computed series yields updated estimates of the model's
critical parameters in good agreement with present renormalization group
estimates.Comment: 3 pages, Latex,(fleqn.sty, espcrc2.sty) no figures, contribution to
Lattice'97 to appear in Nucl. Phys. Proc. Supp
Partially directed paths in a wedge
The enumeration of lattice paths in wedges poses unique mathematical
challenges. These models are not translationally invariant, and the absence of
this symmetry complicates both the derivation of a functional recurrence for
the generating function, and solving for it. In this paper we consider a model
of partially directed walks from the origin in the square lattice confined to
both a symmetric wedge defined by , and an asymmetric wedge defined
by the lines and Y=0, where is an integer. We prove that the
growth constant for all these models is equal to , independent of
the angle of the wedge. We derive functional recursions for both models, and
obtain explicit expressions for the generating functions when . From these
we find asymptotic formulas for the number of partially directed paths of
length in a wedge when .
The functional recurrences are solved by a variation of the kernel method,
which we call the ``iterated kernel method''. This method appears to be similar
to the obstinate kernel method used by Bousquet-Melou. This method requires us
to consider iterated compositions of the roots of the kernel. These
compositions turn out to be surprisingly tractable, and we are able to find
simple explicit expressions for them. However, in spite of this, the generating
functions turn out to be similar in form to Jacobi -functions, and have
natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT
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
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 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.
Force induced triple point for interacting polymers
We show the existence of a force induced triple point in an interacting
polymer problem that allows two zero-force thermal phase transitions. The phase
diagrams for three different models of mutually attracting but self avoiding
polymers are presented. One of these models has an intermediate phase and it
shows a triple point but not the others. A general phase diagram with
multicritical points in an extended parameter space is also discussed.Comment: 4 pages, 8 figures, revtex
Complex-Temperature Singularities in the Ising Model. III. Honeycomb Lattice
We study complex-temperature properties of the uniform and staggered
susceptibilities and of the Ising model on the honeycomb
lattice. From an analysis of low-temperature series expansions, we find
evidence that and both have divergent singularities at the
point (where ), with exponents
. The critical amplitudes at this
singularity are calculated. Using exact results, we extract the behaviour of
the magnetisation and specific heat at complex-temperature
singularities. We find that, in addition to its zero at the physical critical
point, diverges at with exponent , vanishes
continuously at with exponent , and vanishes
discontinuously elsewhere along the boundary of the complex-temperature
ferromagnetic phase. diverges at with exponent
and at (where ) with exponent , and
diverges logarithmically at . We find that the exponent relation
is violated at ; the right-hand side is 4
rather than 2. The connections of these results with complex-temperature
properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a
compressed, uuencoded postscript fil
A strong-coupling analysis of two-dimensional O(N) sigma models with on square, triangular and honeycomb lattices
Recently-generated long strong-coupling series for the two-point Green's
functions of asymptotically free lattice models are
analyzed, focusing on the evaluation of dimensionless renormalization-group
invariant ratios of physical quantities and applying resummation techniques to
series in the inverse temperature and in the energy . Square,
triangular, and honeycomb lattices are considered, as a test of universality
and in order to estimate systematic errors. Large- solutions are carefully
studied in order to establish benchmarks for series coefficients and
resummations. Scaling and universality are verified. All invariant ratios
related to the large-distance properties of the two-point functions vary
monotonically with , departing from their large- values only by a few per
mille even down to .Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi
Low temperature series expansions for the square lattice Ising model with spin S > 1
We derive low-temperature series (in the variable )
for the spontaneous magnetisation, susceptibility and specific heat of the
spin- Ising model on the square lattice for , 2, , and
3. We determine the location of the physical critical point and non-physical
singularities. The number of non-physical singularities closer to the origin
than the physical critical point grows quite rapidly with . The critical
exponents at the singularities which are closest to the origin and for which we
have reasonably accurate estimates are independent of . Due to the many
non-physical singularities, the estimates for the physical critical point and
exponents are poor for higher values of , though consistent with
universality.Comment: 14 pages, LaTeX with IOP style files (ioplppt.sty), epic.sty and
eepic.sty. To appear in J. Phys.
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