Numerical studies of Ising spin glasses in two, three, and four dimensions.
Numerical studies of Ising spin glasses in two, three, and four dimensions.
复制标题
伊辛自旋玻璃在二维、三维和四维上的数值研究。
DOI：
10.1103/physrevb.37.5606
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
A. P. Young
中科院分区：
文献类型：
--
作者：
Ravindra N. Bhatt;A. P. Young
我们提出了伊辛自旋玻璃在零磁场中的数值模拟结果，以及超立方晶格上的最近邻相互作用，在二维、三维和四维上具有高斯和±J键分布。使用有限尺寸缩放来分析结果。在二维 (d= 2) 中，我们同意早期的工作，即转变温度位于 T c= 0，并获得 ±J 模型零温度转变时的相关长度指数 ν 和指数 η。在 d= 3 维中，我们专注于高斯分布的结果，因为我们之前已经给出了 ±J 分布的结果。正如预期的那样，我们发现两个分布的结果相似，即 T c 非零，但有证据表明 d= 3 接近较低的临界维度。在具有高斯键的四维自旋玻璃中，我们发现只需要适量的计算机时间即可证明 T c 不为零且长程有序相低于 T c 。我们对 d= 4 维临界指数的估计与最近高温系列膨胀的结果非常吻合。
We present the results of numerical simulations on Ising spin glasses in zero magnetic field with nearest-neighbor interactions on hyper-cubic lattices in two, three, and four dimensions with both Gaussian and±J bond distributions. Finite-size scaling is used to analyze the results. In two dimensions (d= 2) we agree with earlier work that the transition temperature is at T c= 0, and obtain the correlation-length exponent ν, and the exponent η, at the zero-temperature transition for the±J model. In d= 3 dimensions we concentrate on results for the Gaussian distribution, since our results for the±J distribution have been presented earlier. As expected, we find similar results for the two distributions, namely a nonzero T c but evidence that d= 3 is close to the lower critical dimension. In a four-dimensional spin glass with Gaussian bonds we find that only a modest amount of computer time is required to show that T c is nonzero with a long-range-ordered phase below T c. Our estimates for critical exponents in d= 4 dimensions agree well with results from recent high-temperature-series expansions.