Conjectured exact percolation thresholds of the Fortuin–Kasteleyn cluster for the ±J Ising spin glass model

Chiaki Yamaguchi

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 6, 1263-1268

Abstract: The conjectured exact percolation thresholds of the Fortuin–Kasteleyn cluster for the ±J Ising spin glass model are theoretically shown based on a conjecture. It is pointed out that the percolation transition of the Fortuin–Kasteleyn cluster for the spin glass model is related to a dynamical transition for the freezing of spins. The present results are obtained as locations of points on the so-called Nishimori line, which is a special line in the phase diagram. We obtain TFK=2/ln(z/z−2) and pFK=z/2(z−1) for the Bethe lattice, TFK→∞ and pFK→1/2 for the infinite-range model, TFK=2/ln3 and pFK=3/4 for the square lattice, TFK∼3.9347 and pFK∼0.62441 for the simple cubic lattice, TFK∼6.191 and pFK∼0.5801 for the 4-dimensional hypercubic lattice, and TFK=2/ln[1+2sin(π/18)/1−2sin(π/18)] and pFK=[1+2sin(π/18)]/2 for the triangular lattice, when J/kB=1, where z is the coordination number, J is the strength of the exchange interaction between spins, kB is the Boltzmann constant, TFK is the temperature at the percolation transition point, and pFK is the probability, that the interaction is ferromagnetic, at the percolation transition point.

Keywords: Spin glass; The Fortuin–Kasteleyn cluster; Percolation; Damage spreading; Gauge transformation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:6:p:1263-1268

DOI: 10.1016/j.physa.2012.11.042

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