Diffferent facets of the raise and peel model

The raise and peel model is a one-dimensional stochastic model of a fluctuating interface with nonlocal interactions. This is an interesting physical model, in this paper we review its properties. Its phase diagram has a massive phase and a gapless phase with varying critical exponents. At the phase transition point, the model exhibits conformal invariance which is a space time symmetry. Also at this point the model has several other facets which are the connections to associative algebras, two-dimensional fully packed loop models and combinatorics.