Different facets of the raise and peel model

TL;DR

This paper explores various aspects of the raise and peel model, a stochastic interface model with rich phase behavior, conformal invariance, and connections to algebra, loop models, and combinatorics.

Contribution

It provides a comprehensive analysis of the model's facets, including its phase diagram, conformal invariance, and links to algebraic and combinatorial structures.

Findings

The model has a massive phase and a gapless phase with critical exponents.

At the phase transition, the model exhibits conformal invariance.

Connections to associative algebras and loop models are established.

Abstract

The raise and peel model is a one-dimensional stochastic model of a fluctuating interface with nonlocal interactions. This is an interesting physical model. It's 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.