论文标题
引导Heisenberg磁铁及其立方不稳定性
Bootstrapping Heisenberg Magnets and their Cubic Instability
论文作者
论文摘要
我们使用数值保形引导程序研究了关键的$ O（3）$模型。特别是，我们使用最近开发的切割表面算法来有效地绘制涉及领先的$ o（3）$ s $ s $，vector $ ϕ $和rank-2对称张量$ t $的相关器中的CFT数据允许的空间。我们确定它们的缩放尺寸为$（δ_{s}，δ_ϕ，δ_{t}）=（0.518942（51），1.59489（59），1.20954（23））$，也绑定了各种OPE系数。我们还引入了一种新的“尖端找到”算法，以计算领先的等级4对称张量$ t_4 $的上限，我们发现这与$δ_{t_4} <2.99056 $相关。因此，共形引导程序提供了一个数值证明，即关键$ O（3）$模型所描述的系统，例如Curie Transition的经典Heisenberg Ferromagnets，对立方各向异性不稳定。
We study the critical $O(3)$ model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of CFT data from correlators involving the leading $O(3)$ singlet $s$, vector $ϕ$, and rank-2 symmetric tensor $t$. We determine their scaling dimensions to be $(Δ_{s}, Δ_ϕ, Δ_{t}) = (0.518942(51), 1.59489(59), 1.20954(23))$, and also bound various OPE coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor $t_4$, which we find to be relevant with $Δ_{t_4} < 2.99056$. The conformal bootstrap thus provides a numerical proof that systems described by the critical $O(3)$ model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.
