 02517 Marek Biskup, Lincoln Chayes and Roman Kotecky
 Critical region for droplet formation in the twodimensional Ising model
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Dec 14, 02

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Abstract. We study the formation/dissolution of equilibrium droplets in finite systems at parameters
corresponding to phase coexistence. Specifically, we consider
the 2D Ising model in volumes of size~$L^2$, inverse temperature~$\beta>\betac$
and overall magnetization conditioned to take the value
$\mstar L^22\mstar v_L$, where~$\betac^{1}$
is the critical temperature,~$\mstar=\mstar(\beta)$ is the spontaneous magnetization
and $v_L$ is a sequence of positive numbers.
We find that the critical scaling for droplet formation/dissolution is when~$v_L^{3/2} L^{2}$
tends to a definite limit. Specifically, we identify a dimensionless parameter~$\Delta$,
proportional to this limit, a nontrivial critical value~$\Deltac$ and a function~$\lambda_\Delta$
such that the following holds: For~$\Delta<\Deltac$, there are no droplets beyond~$\log L$ scale,
while for~$\Delta>\Deltac$, there is a single, Wulffshaped droplet containing
a fraction~$\lambda_\Delta\ge\lamc=2/3$ of the magnetization deficit and
there are no other droplets beyond the scale of~$\log L$.
Moreover,~$\lambda_\Delta$ and~$\Delta$ are related via a universal equation that apparently
is independent of the details of the system.
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