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Metastability in the two-dimensional Ising model with free boundary conditions. (English) Zbl 0965.82004

Summary: We investigate metastability in the two-dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit \(T\to 0, h\to 0\) and via Monte Carlo simulations at fixed values of \(T\) and \(h\) and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)

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