发表机构
KAIST（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维SOS模型在淬火无序下的润湿转变，证明淬火临界点与均匀模型一致，且淬火过剩自由能的领先近临界渐近行为与均匀模型相同，均满足u^3标度。
AI 中文摘要
我们研究了在淬火无序存在下，二维固上固（SOS）界面在硬壁之上的润湿转变。该界面由一个非负整数值高度函数$\phi$表示，其哈密顿量为$\mathcal H^\omega(\phi)=\beta\sum_{x\sim y}|\phi(x)-\phi(y)|-\sum_x(h+\alpha\omega_x-\lambda(\alpha))\mathbf 1_{\{\phi(x)=0\}}$，其中$(\omega_x)_{x\in\mathbb Z^2}$是一个独立同分布的中心化场，$\alpha\ge0$是无序强度，$\lambda(\alpha)=\log\mathbb E[e^{\alpha\omega_0}]$。选择这种归一化是为了使退火模型与相应的均匀润湿模型一致。随着壁吸引力$h$的增加，界面经历从去局域相（与壁接触密度趋于零）到局域相（接触密度为正）的转变。对于足够大的$\beta$，均匀润湿点及其尖锐的近临界自由能行为是已知的。我们证明，对于每个固定的$\alpha\ge0$，淬火临界点与均匀润湿点重合，即$h_c(\beta,\alpha)=h_w(\beta)=-\log(1-e^{-4\beta})$。此外，记$u=h-h_w(\beta)$，我们证明淬火过剩自由能满足$\overline F_\beta(\alpha,u)=\overline F_{\mathrm{homo}}(\beta,u)+o(u^3)$当$u\downarrow0$时，其中$\overline F_{\mathrm{homo}}(\beta,u)$表示领先的均匀润湿渐近行为，且满足$\overline F_{\mathrm{homo}}(\beta,u)\asymp u^3$。因此，在临界点和领先的近临界自由能渐近行为层面，淬火模型与均匀SOS润湿模型具有相同的行为。这与无序SOS钉扎模型形成对比，在后者中，淬火无序不改变临界点，但改变了自由能的领先临界行为。
英文摘要
We study the wetting transition for a two-dimensional Solid-On-Solid (SOS) interface above a hard wall in the presence of quenched disorder. The interface is represented by a nonnegative integer-valued height function $ϕ$, with Hamiltonian $\mathcal H^ω(ϕ)=β\sum_{x\sim y}|ϕ(x)-ϕ(y)|-\sum_x(h+αω_x-λ(α))\mathbf 1_{\{ϕ(x)=0\}}$, where $(ω_x)_{x\in\mathbb Z^2}$ is an i.i.d. centered field, $α\ge0$ is the disorder strength, and $λ(α)=\log\mathbb E[e^{αω_0}]$. This normalization is chosen so that the annealed model coincides with the corresponding homogeneous wetting model. As the wall attraction $h$ increases, the interface undergoes a transition from a delocalized phase, in which contacts with the wall have vanishing density, to a localized phase with a positive density of contacts. For sufficiently large $β$, the homogeneous wetting point and its sharp near-critical free-energy behavior are known. We prove that, for every fixed $α\ge0$, the quenched critical point coincides with the homogeneous wetting point, $h_c(β,α)=h_w(β)=-\log(1-e^{-4β})$. Moreover, writing $u=h-h_w(β)$, we show that the quenched excess free energy satisfies $\overline F_β(α,u)=\overline F_{\mathrm{homo}}(β,u)+o(u^3)$ as $u\downarrow0$, where $\overline F_{\mathrm{homo}}(β,u)$ denotes the leading homogeneous wetting asymptotic and satisfies $\overline F_{\mathrm{homo}}(β,u)\asymp u^3$. Thus, at the level of both the critical point and the leading near-critical free-energy asymptotics, the quenched model has the same behavior as the homogeneous SOS wetting model. This contrasts with the disordered SOS pinning model, in which quenched disorder leaves the critical point unchanged but modifies the leading critical behavior of the free energy.
Comments48 pages, no figure
