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Evaporation/Condensation of Ising Droplets

Andreas Nussbaumer·Elmar Bittner·Wolfhard Janke
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Abstract

Recently Biskup et al. [Europhys. Lett. 60 (2002) 21] studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $δN$ of particles above the ambient gas density. They identify a dimensionless parameter $Δ(δN)$ and a universal constant $Δ_\mathrm{c}(d)$ and show that for $Δ< Δ_c$ a droplet of the dense phase occurs while for $Δ> Δ_c$ the excess is absorbed in the background. The fraction $λ_Δ$ of excess particles forming the droplet is given explicitly. Furthermore, they state, that the same is true for solid-gas systems. To verify these results, we have simulated the spin-1/2 Ising model on a square lattice at constant magnetisation equivalent to a fixed particle excess in the lattice-gas picture. We measured the largest minority droplet, corresponding to the solid phase, at various system sizes ($L=40, ..., 640$). Using analytic values for the spontaneous magnetisation $m_0$, the susceptibility $χ$ and interfacial free energy $τ_\mathrm{W}$ for the infinite system, we were able to determine $λ_Δ$ in very good agreement with the theoretical prediction.

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Andreas Nussbaumer, Elmar Bittner, Wolfhard Janke. 2005-09-23. Evaporation/Condensation of Ising Droplets. https://arxiv.org/abs/hep-lat/0509112

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