Teil eines Buches,
The evaporation/condensation transition of Ising droplets
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Zusammenfassung
In recent analytical work, Biskup et al. Europhys.\ Lett. 60 (2002) 21 studied the behaviour of $d$-dimensional liquid-vapour systems at a fixed excess $N$ of
particles above the ambient gas density in the infinite-volume limit.
By identifying a
dimensionless parameter $\Delta (N)$ and a universal constant
$\Delta_c(d)$, they showed that for $\Delta < \Delta_c$ the
excess is absorbed in the background (``evaporated'' system), while
for $\Delta > \Delta_c$ a droplet of the dense phase occurs
(``condensed'' system). Also the fraction $łambda_\Delta$ 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 and a triangular lattice with periodic boundary conditions at fixed
magnetisation, corresponding to a fixed particles excess. To study
the approach to the asymptotic formulas,
we measured the largest minority droplet,
corresponding to the solid phase, for various system sizes.
Using analytic values for the spontaneous
magnetisation $m_0$, the susceptibility $\chi$ and the Wulff
interfacial free energy density $\tau_W$ for the infinite system,
we obtain for both lattice types extrapolations of $łambda_\Delta$ in very good
agreement with the theoretical prediction.
