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Elmar Bittner, Andreas Nussbaumer and Wolfhard Janke,
The formation and dissolution of equilibrium droplets at a first-order phase transition is one of the longstanding problems in statistical mechanics. Quantities of particular interest are the size and free energy of a 'critical droplet' that needs to be formed before the decay of the metastable state via homogeneous nucleation can start. For large but finite systems, this is signalised by a cusp in the probability density of the order parameter $\phi$ towards the phase-coexistence region. This cusp is often termed evaporation/condensation 'transition point' since it separates an 'evaporated' phase with many very small bubbles of the 'wrong' phase around the peak at $\phi_0$ from the 'condensed' phase, in which a large droplet has formed. This two-phase state is studied for the 2D spin-1/2 Ising model, with the use of Monte Carlo methods. We have simulated on a square lattice at constant magnetisation equivalent to a fixed particle excess in the lattice-gas picture. Thereby, we measured the largest minority droplet at various system sizes and compared our results with the theoretical prediction for the infinite system of Biskup et al. [Commun. Math. Phys. 242, 137 (2003)]. For the 2D Ising model with nearest-neighbor couplings the observed finite-size scaling behavior fits perfectly with their predictions. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbour couplings on a square lattice. Again, finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice and type of interactions. |
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