标题： 分支界面与无限强耦合 显示英文标题

标题： Branching Interfaces with Infinitely Strong Couplings

摘要： 一个随机$q$-态 Potts 铁磁体在$2D$中的界面的分层泡沫模型通过递归方法进行研究。 通过无限强的铁磁耦合，使最近邻键中的分数$p$对畴壁不可达。 界面的能量和几何标度性质由零温度固定分布控制。 对于$p<p_c$，即定向渗透阈值，界面表现得如同对于$p=0$，并且标度支持所有$q$的随机伊辛（$q=2$）临界行为。 在$ p=p_c$处，对于铁磁与反铁磁耦合的不同比例，获得了三种状态。 当速率高于阈值时，界面是线性的（分形维数$d_f=1$），其能量波动，$\Delta E$随长度按$\Delta E\propto L^{\omega}$的方式变化，其中$\omega\simeq 0.48$。 当达到阈值时，界面在所有尺度上分支并且是分形的（$d_f\simeq 1.046$），其中$\omega_c \simeq 0.51$。 因此，在$p_c$处，稀释同时改变了低温界面性质和临界标度。低于阈值时，界面成为骨架几何结构的探测器 ($\df\simeq{\bar d}\simeq 1.305$;$\bar d$= 骨架分形维数 )，这甚至控制了能量涨落 ($\omega\simeq d_f\simeq\bar d$)。还给出了在金刚石分形格子上定向渗透指数的数值确定结果。 显示英文摘要

摘要： A hierarchical froth model of the interface of a random $q$-state Potts ferromagnet in $2D$ is studied by recursive methods. A fraction $p$ of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings. Energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions. For $p<p_c$, the directed percolation threshold, the interface behaves as for $p=0$, and scaling supports random Ising ($q=2$) critical behavior for all $q$'s. At $ p=p_c$ three regimes are obtained for different ratios of ferro vs. antiferromagnetic couplings. With rates above a threshold value the interface is linear ( fractal dimension $d_f=1$) and its energy fluctuations, $\Delta E$ scale with length as $\Delta E\propto L^{\omega}$, with $\omega\simeq 0.48$. When the threshold is reached the interface branches at all scales and is fractal ($d_f\simeq 1.046$) with $\omega_c \simeq 0.51$. Thus, at $p_c$, dilution modifies both low temperature interfacial properties and critical scaling. Below threshold the interface becomes a probe of the backbone geometry ($\df\simeq{\bar d}\simeq 1.305$; $\bar d$ = backbone fractal dimension ), which even controls energy fluctuations ($\omega\simeq d_f\simeq\bar d$). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.