Europhys. Lett.
Volume 75, Number 5, September 2006
Page(s) 716 - 722
Section General
Published online 10 August 2006
Europhys. Lett., 75 (5), pp. 716-722 (2006)
DOI: 10.1209/epl/i2006-10190-9

Monte Carlo study of the evaporation/condensation transition of Ising droplets

A. Nußbaumer1, E. Bittner1, T. Neuhaus2 and W. Janke1

1  Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ) Universität Leipzig - Augustusplatz 10/11, D-04109 Leipzig, Germany
2  John von Neumann-Institut für Computing, Forschungszentrum Jülich D-52425 Jülich, Germany

received 7 May 2006; accepted in final form 18 July 2006
published online 10 August 2006

In recent analytical work, Biskup et al. (Europhys. Lett., 60 (2002) 21) studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $\delta N$ of particles above the ambient gas density. By identifying a dimensionless parameter $\Delta (\delta N)$ and a universal constant $\Delta_{\rm c}(d)$, they showed in the limit of large system sizes that for $\Delta < \Delta_{\rm c}$ the excess is absorbed in the background ("evaporated" system), while for $\Delta > \Delta_{\rm c}$ a droplet of the dense phase occurs ("condensed" system). Also the fraction $\lambda_\Delta$ of excess particles forming the droplet is given explicitly. Furthermore, they argue that the same is true for solid-gas systems. By making use of the well-known equivalence of the lattice-gas picture with the spin-(1/2) Ising model, we performed Monte Carlo simulations of the Ising model with nearest-neighbour couplings on a square lattice with periodic boundary conditions at fixed magnetisation, corresponding to a fixed particles excess. To test the applicability of the analytical results to much smaller, practically accessible system sizes, we measured the largest minority droplet, corresponding to the solid phase, at various system sizes ( $L=40,
\ldots, 640$). Using analytic values for the spontaneous magnetisation m0, the susceptibility $\chi$ and the Wulff interfacial free energy density $\tau_{\rm W}$ for the infinite system, we were able to determine $\lambda_\Delta$ numerically in very good agreement with the theoretical prediction.

05.70.Fh - Phase transitions: general studies.
02.70.Uu - Applications of Monte Carlo methods.
75.10.Hk - Classical spin models.

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