A direct proof of Kim's identities

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics

Tetromino tilings and the Tutte polynomial

We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polynomial Z\_G(Q,v) (known also to physicists as the partition function of the Q-state Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure

Bethe Equations "on the Wrong Side of Equator"

We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution which should corresponds to Bethe-Ansatz beyond $N/2$. This second solution of Baxter's equation plays essential role and together with the first one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio

Bethe Ansatz Equations for the Broken ZNZ_{N}-Symmetric Model

We obtain the Bethe Ansatz equations for the broken ${\bf Z}_{N}$-symmetric model by constructing a functional relation of the transfer matrix of $L$-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov model. We calculate the free energy of this model on the basis of the string hypothesis.Comment: 43 pages, latex, 11 figure

Entropy of Folding of the Triangular Lattice

The problem of counting the different ways of folding the planar triangular lattice is shown to be equivalent to that of counting the possible 3-colorings of its bonds, a dual version of the 3-coloring problem of the hexagonal lattice solved by Baxter. The folding entropy Log q per triangle is thus given by Baxter's formula q=sqrt(3)(Gamma[1/3])^(3/2)/2pi =1.2087...Comment: 9 pages, harvmac, epsf, uuencoded, 5 figures included, Saclay preprint T/9401

Selfduality for coupled Potts models on the triangular lattice

We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points

Sexual negotiation in the AIDS era: negotiated safety revisited

Objective: To test the safety of the 'negotiated safety' strategy - the strategy of dispensing with condoms within HIV-seronegative concordant regular sexual relationships under certain conditions. Method: Data from a recently recruited cohort of homosexually active men (Sydney Men and Sexual Health cohort, n = 1037) are used to revisit negotiated safety. The men were surveyed using a structured questionnaire and questions addressing their sexual relationships and practice, their own and their regular partner's serostatus, agreements entered into by the men concerning sexual practice within and outside their regular relationship, and contextual and demographic variables. Results: The findings indicate that a significant number of men used negotiated safety as an HIV prevention strategy. In the 6 months prior to interview, of the 181 men in seroconcordant HIV-negative regular relationships, 62% had engaged in unprotected anal intercourse within their relationship, and 91% (165 men) had not engaged in unprotected anal intercourse outside their relationship. Of these 165 men, 82% had negotiated agreements about sex outside their relationship. The safety of negotiation was dependent not only on seroconcordance but also on the presence of an agreement; 82% of the men who had not engaged in unprotected anal intercourse outside their regular relationship had entered into an agreement with their partner, whereas only 56% of those who had engaged in unprotected anal intercourse had an agreement. The safety of negotiation was also related to the nature of the safety agreement reached between the men and on the acceptability of condoms. Agreements between HIV-negative seroconcordant regular partners prohibiting anal intercourse with casual partners or any form of sex with a casual partner were typically complied with, and men who had such negotiated agreements were at low risk of HIV infection. Conclusions: The adoption of the strategy of negotiated safety among men in HIV-seronegative regular relationships may help such men sustain the safety of their sexual practice

Buoyant Venus station feasibility study. Volume IV - Communications and power Final report

Telecommunication and power supply requirements for inflatable buoyant Venus statio