Ising model

The Ising Model in Curved Geometries

SLIDES The study of statistical mechanics in curved geometries has recently gained an increasing amount of attention. Particularly the Ising model in negatively curved spaces has been studied as a mean to understand exotic crystals, soft-matter and field theories in Anti-de Sitter spaces. We analyze the Ising model on in the hyperbolic plane as well as 2+1-Anti-de Sitter (AdS) space using high temperature series-expansion and Monte-Carlo simulations. While series expansions have been performed on the hyperbolic plane before, we study a wider class of hyperbolic lattices and go to much higher order, allowing us to analyze the dependency of critical phenomena on the magnitude of curvature.