Critical region for droplet formation in the two-dimensional Ising model

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dc.creatorBiskup, Marek
dc.creatorChayes, Lincoln
dc.creatorKotecky, Roman
dc.date2002-12-21
dc.date2003-09-30
dc.date.accessioned2026-07-07T04:53:58Z
dc.date.available2026-07-07T04:53:58Z
dc.descriptionWe 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 $β>\betac$ and overall magnetization conditioned to take the value $\mstar L^2-2\mstar v_L$, where $\betac^{-1}$ is the critical temperature, $\mstar=\mstar(β)$ 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 $Δ$, proportional to this limit, a non-trivial critical value $\Deltac$ and a function $λ_Δ$ such that the following holds: For $Δ<\Deltac$, there are no droplets beyond $\log L$ scale, while for $Δ>\Deltac$, there is a single, Wulff-shaped droplet containing a fraction $λ_Δ\ge\lamc=2/3$ of the magnetization deficit and there are no other droplets beyond the scale of $\log L$. Moreover, $λ_Δ$ and $Δ$ are related via a universal equation that apparently is independent of the details of the system.
dc.description48 pages, 2 figures, version to appear in Commun. Math. Phys
dc.identifierhttps://arxiv.org/abs/math/0212300
dc.identifierhttp://arxiv.org/abs/math/0212300
dc.identifierCommun. Math. Phys. 242 (2003), no. 1-2, 137--183
dc.identifierdoi:10.1007/s00220-003-0946-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66066
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectChemical Physics
dc.subject60F10; 82B05; 82B24
dc.titleCritical region for droplet formation in the two-dimensional Ising model
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