We address the question of weak versus strong universality scenarios for therandom-bond Ising model in two dimensions. A finite-size scaling theory isproposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linearfinite size of the system) to the temperature derivative of the correlationlength. The predictions are tested by considering long, finite-width strips ofIsing spins with randomly distributed ferromagnetic couplings, along which freeenergy, spin-spin correlation functions and specific heats are calculated bytransfer-matrix methods. The ratio $\gamma/\nu$ is calculated and has the samevalue as in the pure case; consequently conformal invariance predictions remainvalid for this type of disorder. Semilogarithmic plots of correlation functionsagainst distance yield average correlation lengths $\xi^{av}$, whose sizedependence agrees very well with the proposed theory. We also examine the sizedependence of the specific heat, which clearly suggestsa divergency in thethermodynamic limit. Thus our data consistently favour the Dotsenko-Shalaevpicture of logarithmic corrections (enhancements) to pure system singularities,as opposed to the weak universality scenario.
展开▼
机译：我们在两个维度上解决了随机键伊辛模型的普遍性弱弱问题。提出了一种有限大小的比例缩放理论，该理论将$ \ ln L $校正（$ L $是系统的线性有限大小）显式合并到相关长度的温度导数中。通过考虑带有有限分布的铁磁耦合的Ising自旋的有限长条形带测试预言，沿着该带，通过转移矩阵法计算自由能，自旋-自旋相关函数和比热。计算比率$ \ gamma / \ nu $并具有与纯情况下相同的值；因此，共形不变性预测对于这种类型的疾病仍然有效。相关函数对距离的半对数图产生平均相关长度$ \ xi ^ {av} $，其大小依赖性与所提出的理论非常吻合。我们还检查了比热的大小依赖性，这清楚地表明了热力学极限存在差异。因此，我们的数据始终支持纯系统奇点的对数校正（增强）的Dotsenko-Shalaev图，而不是弱通用性情形。
展开▼
