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arXiv 1503.02103cond-mat.dis-nncond-mat.stat-mech
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自旋玻璃中的非微扰效应

Non-perturbative effects in spin glasses

Michele Castellana, Giorgio Parisi

摘要:

本文对具有分级相互作用的Ising自旋玻璃--具有外磁场的分级Edwards-Anderson模型(HEA)进行了数值研究。在平均场(MF)和非平均场(NMF)区域分别对$d$维铁磁伊辛模型的$d\geq4$和$d<4$进行了蒙特卡罗(MC)模拟.我们比较MC的结果与重整化群(RG)的研究,其中的临界不动点被视为一个扰动的MF的,沿着相同的线在$ε$ -扩展的伊辛模型。MC和RG方法同意在MF区域,预测存在的过渡和兼容值的临界指数。相反,这两种方法显着不同意在NMF的情况下,MC数据表明过渡,而RG分析预测,没有微扰临界不动点存在。此外,MC估计的临界指数$ν$在NMF区域是大约两倍大,其经典值,即使模拟的系统尺寸是从它的上限临界尺寸值只有$\sim 2\%$。总之,这些结果表明,在NMF区域的过渡是由强非微扰效应。

英文摘要:

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 $d\geq4$ 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 $ε$-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 $\sim 2\%$ 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.

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