Series studies of the Potts model. I: The simple cubic Ising model

The finite lattice method of series expansion is generalised to the $q$-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 ($q=2$) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. 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 $\kappa(z)$ to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity $z_d$ which lies on on the negative fugacity axis. We find that the series has a confluent singularity of order 2 at $z_d$ with exponents $\theta=0.83333(2)$ and $\theta'= 1.6676(3)$. We thus confirm that the exponent $\theta$ has the exact value $\frac56$ 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 $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, 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 $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, 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 $\sqrt{2+\sqrt{2}}.$ 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