Castellana Michele, Parisi Giorgio
Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, United States.
Dipartimento di Fisica, Università Sapienza, Rome, Italy.
Sci Rep. 2015 Mar 3;5:8697. doi: 10.1038/srep08697.
We present a numerical study of an Ising spin glass with hierarchical interactions--the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the -expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.
我们对具有层次相互作用的伊辛自旋玻璃——带外磁场的层次爱德华兹 - 安德森模型（HEA）进行了数值研究。我们分别在与(d)维铁磁伊辛模型中(d\geq4)和(d\lt4)相对应的平均场（MF）和非平均场（NMF）区域，用蒙特卡罗（MC）模拟研究该模型。我们将MC结果与重整化群（RG）研究的结果进行比较，在RG研究中，临界不动点被视为MF不动点的微扰，这与伊辛模型的(\epsilon)展开中的做法相同。MC和RG方法在MF区域结果一致，预测了相变的存在以及临界指数的兼容值。相反，在NMF情况下，这两种方法明显不同，MC数据表明存在相变，而RG分析预测不存在微扰临界不动点。此外，即使系统维度的类似值仅比其上临界维度值小约2%，NMF区域中临界指数(\nu)的MC估计值也约为其经典值的两倍。综合来看，这些结果表明NMF区域中的相变受强非微扰效应支配。
