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Exact ground states of two-dimensional \(\pm J\) Ising spin glasses. (English) Zbl 1260.82083

Summary: In this paper we study the problem of finding an exact ground state of a two-dimensional \(\pm J\) Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentration \(p\) of negative bonds, with \(p\) ranging between \(0.1\) and \(0.9\). With our exact algorithm we can determine ground states of grids of sizes up to \(50\times 50\) in a moderate amount of compution time (up to \(1\) hr each) for several values of \(p\). For the ground-state energy of an infinite spin-glass system with \(p=0.5\) we estimate \(E_{0.5}^{\infty}=-1.4015\pm 0.0008\). We report on extensive computational tests based on more than 22,000 experiments.

MSC:

82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

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