Abstract
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of -state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum-stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum-information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and high-low temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width.
- Received 22 November 2006
DOI:https://doi.org/10.1103/PhysRevLett.98.117207
©2007 American Physical Society