Graphical Representations for Ising Systems in External Fields

Details Graphical Representations for Ising Systems in External Fields Graphical Representations for Ising Systems in External Fields

1998-06-25

arxiv.org/abs/cond-mat/9806312v1

J. Stat. Phys. 93:17-32 (1998)

Physics

Condensed Matter

Statistical Mechanics

13 pages amstex

Scientific paper

10.1023/B:JOSS.0000026726.43558.

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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