text: 177,97,1170926863214137344,985110481345155072,Eren M. Elçi,"Often it’s a useful strategy to embed a math problem into a larger space to solve it. In this paper we use this idea and construct a new coupling of „geometric“ representations of the random-cluster model to design a new MCMC algorithm for the RC-model. <LINK> Beyond it’s application to design a new MCMC algorithm, we can use our coupling to construct a perfect sampling algorithm for the q-flow representation of the Potts model. This uses the idea of coupling of MCMC chains, see here our work here: <LINK> <LINK>",http://arxiv.org/abs/1909.02719,"Potts spin systems play a fundamental role in statistical mechanics and quantum field theory, and can be studied within the spin, the Fortuin-Kasteleyn (FK) bond or the $q$-flow (loop) representation. We introduce a Loop-Cluster (LC) joint model of bond-occupation variables interacting with $q$-flow variables, and formulate a LC algorithm that is found to be in the same dynamical universality as the celebrated Swendsen-Wang algorithm. This leads to a theoretical unification for all the representations, and numerically, one can apply the most efficient algorithm in one representation and measure physical quantities in others. Moreover, by using the LC scheme, we construct a hierarchy of geometric objects that contain as special cases the $q$-flow clusters and the backbone of FK clusters, the exact values of whose fractal dimensions in two dimensions remain as an open question. Our work not only provides a unified framework and an efficient algorithm for the Potts model, but also brings new insights into rich geometric structures of the FK clusters. ",Loop-Cluster Coupling and Algorithm for Classical Statistical Models,3,"['Often it’s a useful strategy to embed a math problem into a larger space to solve it. In this paper we use this idea and construct a new coupling of „geometric“ representations of the random-cluster model to design a new MCMC algorithm for the RC-model. <LINK>', 'Beyond it’s application to design a new MCMC algorithm, we can use our coupling to construct a perfect sampling algorithm for the q-flow representation of the Potts model. This uses the idea of coupling of MCMC chains, see here our work here: https://t.co/msiDh1kWvl', 'https://t.co/kLljH3R3Qm']",19,09,517