The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing autocorrelation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

中文翻译：

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来自量子蒙特卡罗模拟的长程横向场 Ising 模型的量子临界性质

通过随机级数展开量子蒙特卡罗，在一维线性链和二维方格上研究了具有代数衰减相互作用的横向场 Ising 模型的量子临界性质。我们提取关键指数$\nu$ 和 $\beta$作为长程相互作用的衰减指数的函数。对于铁磁 Ising 相互作用，我们解决了从场论中已知的限制机制，从最近邻 Ising 到远程高斯普遍性类，以及具有连续变化的临界指数的中间机制。在长程高斯机制中，我们处理危险的无关变量对有限大小缩放形式的影响。对于反铁磁和因此竞争的 Ising 相互作用，随机级数展开算法显示出不断增长的自相关时间，从而导致性能降低。尽管如此，我们的结果与线性链和方形晶格上所有研究的相互作用范围的最近邻 Ising 普遍性一致。