1,625 research outputs found
Series studies of the Potts model. I: The simple cubic Ising model
The finite lattice method of series expansion is generalised to the -state
Potts model on the simple cubic lattice.
It is found that the computational effort grows exponentially with the square
of the number of series terms obtained, unlike two-dimensional lattices where
the computational requirements grow exponentially with the number of terms. For
the Ising () case we have extended low-temperature series for the
partition functions, magnetisation and zero-field susceptibility to
from . The high-temperature series for the zero-field partition
function is extended from to . Subsequent analysis gives
critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24
page
Use of Discrete Choice Experiments in health economics: An update of the literature
The vast majority of stated preference research in health economics has been conducted in the random utility model paradigm using discrete choice experiments (DCEs). Ryan and Gerard (2003) have reviewed the applications of DCEs in the field of health economics. We have updated this initial work to include studies published between 2001 and 2007. Following the methods of Ryan and Gerard, we assess the later body of work, with respect to the key characteristics of DCEs such as selection of attributes and levels, experimental design, preference measurement, estimation procedure and validity. Comparisons between the periods are undertaken in order to identify any emerging trends.discrete choice experiments, health economics
Comment on `Series expansions from the corner transfer matrix renormalization group method: the hard-squares model'
Earlier this year Chan extended the low-density series for the hard-squares
partition function to 92 terms. Here we analyse this extended
series focusing on the behaviour at the dominant singularity which lies
on on the negative fugacity axis. We find that the series has a confluent
singularity of order 2 at with exponents and
. We thus confirm that the exponent has the exact
value as observed by Dhar.Comment: 5 pages, 1 figure, IoP macros. Expanded second and final versio
A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice
We present a new and more efficient implementation of transfer-matrix methods
for exact enumerations of lattice objects. The new method is illustrated by an
application to the enumeration of self-avoiding polygons on the square lattice.
A detailed comparison with the previous best algorithm shows significant
improvement in the running time of the algorithm. The new algorithm is used to
extend the enumeration of polygons to length 130 from the previous record of
110.Comment: 17 pages, 8 figures, IoP style file
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
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.
A numerical adaptation of SAW identities from the honeycomb to other 2D lattices
Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by
Nienhuis that the connective constant of self-avoiding walks on the honeycomb
lattice is A key identity used in that proof depends on
the existence of a parafermionic observable for self-avoiding walks on the
honeycomb lattice. Despite the absence of a corresponding observable for SAW on
the square and triangular lattices, we show that in the limit of large
lattices, some of the consequences observed on the honeycomb lattice persist on
other lattices. This permits the accurate estimation, though not an exact
evaluation, of certain critical amplitudes, as well as critical points, for
these lattices. For the honeycomb lattice an exact amplitude for loops is
proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis,
giving greater precision. Explanation of why we observe what we do. Extra
reference
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