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1988•Physical review. B, Condensed matterRequires access

Nonlocal percolation in an antiferromagnetic Potts model

H Fried, M. Schick

Open publisher page 15 citations

Abstract

We devise an algorithm to determine the critical site-occupation probability, ${x}_{c}$, at which antiferromagnetic order in the three-state Potts model first propagates on a triangular lattice. We find ${x}_{c}=0.735$, larger than the value of 0.5 necessary to percolate ferromagnetic order. Even though the means to propagate the order in this problem can be nonlocal as well as local, our results for critical exponents indicate that the percolation transition is in the same universality class as that of ferromagnetic percolation.

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What this paper is about

We devise an algorithm to determine the critical site-occupation probability, ${x}_{c}$, at which antiferromagnetic order in the three-state Potts model first propagates on a triangular lattice. We find ${x}_{c}=0.735$, larger than the value of 0.5 necessary to percolate ferromagnetic order. Even though the means to propagate the order in this problem can be nonlocal as well as local, our results for critical exponents indicate that the percolation transition is in the same universality class as that of ferromagnetic percolation.

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Available abstract

We devise an algorithm to determine the critical site-occupation probability, ${x}_{c}$, at which antiferromagnetic order in the three-state Potts model first propagates on a triangular lattice. We find ${x}_{c}=0.735$, larger than the value of 0.5 necessary to percolate ferromagnetic order. Even though the means to propagate the order in this problem can be nonlocal as well as local, our results for critical exponents indicate that the percolation transition is in the same universality class as that of ferromagnetic percolation.

Key concepts: Potts model, Antiferromagnetism, Percolation critical exponents, Condensed matter physics, Critical exponent, Ferromagnetism, Percolation threshold, Percolation (cognitive psychology)

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