Graphical Representations for Ising Systems in External Fields
L. Chayes (UCLA), J. Machta (UMass), and O. Redner (Tubingen)
TL;DR
This paper introduces a graphical representation for Ising systems in external fields, enabling analysis via percolation and facilitating the development of cluster algorithms for these models.
Contribution
It develops a duplication-based graphical representation for Ising systems in external fields, linking it to Ashkin-Teller models and percolation theory.
Findings
Ordering corresponds to percolation in the graphical model
The representation enables the creation of cluster algorithms
Applications of the representation are discussed
Abstract
A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state (Ashkin-Teller) model. Bonds in the graphical representation connect the Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is characterized by percolation in this representation. The representation leads immediately to cluster algorithms; some applications along these lines are discussed.
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