Sampling from the Gibbs distribution is a well studied problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model and the hard-core model with fugacity λ when the underlying graph is an instance of Erdős-Rényi random graph G(n, p), where p = d/n and d is fixed. We use the Markov Chain Monte Carlo method for sampling from the aforementioned dist...

We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of polymer passing on top of each other. Each polygon configuration can be viewed as the two-dimensional projection of a particular knot. We study numerically th...

Subduction zone or arc magmas are known to display a characteristic depletion of High Field Strength Elements (HFSE) relative to other similarly incompatible elements, which can be attributed to the presence of the accessory mineral rutile (TiO2) in the residual slab. Here we show that the partitioning behavior of vanadium between rutile and silicate melt varies from incompatible (∼0.1) to comp...

Martian meteorites are the only available samples that can be directly measured to constrain geological evolution of Mars. It has been suggested oxygen fugacity (fO2) martian shergottite meteorites, which have low (∼7 wt.%) high-MgO (∼30 compositions, correlates with incompatible trace element enrichment (i.e., La/Yb), and 87Sr/86Sr, 143Nd/144Nd, 187Os/188Os 176Hf/177Hf at time crystallization....