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arXiv · 1905.04220

Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model

Hauke Fajen·Alexander K. Hartmann·A. Peter Young
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Abstract

We apply generalisations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional $\pm 1$ random-bond Ising model. The behaviour of the model is determined by the temperature $T$ and the concentration $p$ of negative (anti-ferromagnetic) bonds. The ground state is ferromagnetic for $0 \le p 0$, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for $p=0$ where the clusters are tied to Ising correlations so the percolation transition is in the Ising universality class.

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Hauke Fajen, Alexander K. Hartmann, A. Peter Young. 2019-05-10. Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model. https://doi.org/10.1103/physreve.102.012131

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