Phase diagrams of period-4 spin chains consisting of three kinds of spins

We study a period-4 antiferromagnetic mixed quantum spin chain consisting of three kinds of spins. When the ground state is singlet, the spin magnitudes in a unit cell are arrayed as (s-t, s, s+t, s) with integer or half-odd integer s and t (0 <= t < s). The spin Hamiltonian is mapped onto a nonlinear sigma model (NLSM) in a previously developed method. The resultant NLSM includes only two independent parameters originating from four exchange constants for fixed s and t. The topological angle in the NLSM determines the gapless phase boundaries between disordered phases in the parameter space. The phase diagrams for various s and t shows rich structures. We systematically explain the phases in the singlet-cluster-solid picture.Comment: 8 pages (16 figures included

Risk reduction and perceived collective efficacy and community support among female sex workers in Tamil Nadu and Maharashtra, India: the importance of context

Background Empowering sex workers to mobilise and influence the structural context that obstructs risk reduction efforts is now seen an essential component of successful HIV prevention programmes. However, success depends on local programme environments and history. Methods The authors analysed data from the Integrated Behavioural and Biological Assessment Round I cross-sectional survey among female sex workers in Tamil Nadu and Maharashtra. The authors used propensity score matching to estimate the impact of participation in intervention activities on reduction of risk (consistent condom use) and vulnerability (perceived collective efficacy and community support). Results Background levels of risk and vulnerability as well as intervention impact varied widely across the different settings. The effect size ATT of attending meetings/trainings on consistent condom use was as high as 21% in Tamil Nadu (outside of Chennai) where overall use was lowest at 51%. Overall, levels of perceived collective efficacy were low at the time of the survey; perceived community support was high in Tamil Nadu and especially in Chennai (93%) contrasting with 33% in Mumbai. Consistent with previous research, the context of Mumbai seems least conducive to vulnerability reduction, yet self-help groups had a significant impact on consistent condom use (ATT=10%) and were significantly associated with higher collective efficacy (ATT=31%). Conclusions Significant risk reduction can be achieved by large-scale female sex worker interventions, but the impact depends on the history of programming, the complexity of the context in which sex work happens and pre-existing levels of support sex workers perceive from their peers