Cluster scaling geometry in critical spin systems

J. F. Marko*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The fractal dimensions of the largest clusters of like spins connected by nearest-neighbor bonds in the critical two-dimensional Q-state Potts model have been determined via Monte Carlo simulations to be df=1.946(3), 1.922(5), and 1.909(8) for Q=2, 3, and 4, respectively. These dimensions are close to the magnetic tricritical exponents of the (Q-1)-state dilute Potts model (d-x=187/96=1.947..., 77/40=1.925, and 40/21=1.904... for Q-1=1, 2, and 3, respectively). The critical Q-state model and the tricritical (Q-1)-state model are related to a two-component Potts lattice gas; this model generates percolative susceptibilities of critical Potts clusters, and suggests a renormalization-group argument for df=d-x.

Original languageEnglish (US)
Pages (from-to)5023-5026
Number of pages4
JournalPhysical Review B
Issue number9
StatePublished - 1992

ASJC Scopus subject areas

  • Condensed Matter Physics


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