自平均和临界性：二维随机键自旋模型的比较研究
Self-averaging and criticality: A comparative study in 2d random bond spin models
摘要：
通过Wang-Landau（WL）算法，研究了猝灭键随机性对二维Ising自旋模型自平均性质的影响.研究了具有最近邻和次最近邻竞争相互作用的超反铁磁（SAF）正方形模型的随机键形式和相应的简单铁磁伊辛模型.我们发现，随机键SAF模型表现出强烈的违反自平均，远远强于观察到的情况下的随机键伊辛模型。我们对样本相关伪临界温度分布方差的渐进标度行为的分析发现与Aharony和Harris的重整化群预测一致。使用这种替代方法，我们发现的相关长度指数$ν$的估计与从通常的有限尺寸标度（FSS）方法获得的结果一致。
英文摘要：
We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple ferromagnetic Ising model are studied. We find that, the random bond SAF model shows a strong violation of self-averaging, much stronger than that observed in the case of the random bond Ising model. Our analysis of the asymptotic scaling behavior of the variance of the distribution of the sample-dependent pseudocritical temperatures is found to be consistent with the renormalization group prediction of Aharony and Harris. Using this alternative approach, we find estimates of the correlation length exponent $ν$ in agreement with results obtained from the usual finite-size scaling (FSS) methodology.
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