Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents
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DOI：
10.1007/s10955-014-1042-7
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发表时间：
2012-03
影响因子：
1.6
通讯作者：
S. El-Showk;M. Paulos;David Poland;S. Rychkov;D. Simmons-Duffin;A. Vichi
中科院分区：
文献类型：
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作者：
S. El-Showk;M. Paulos;David Poland;S. Rychkov;D. Simmons-Duffin;A. Vichi
我们利用共形自举方法对临界三维伊辛模型的算符谱进行了精确研究。我们猜想3D Ising谱使交叉对称的酉解空间中的中心电荷最小化。因为交叉对称的极解是唯一确定的，所以我们能够精确地重构前几个偶数算符的维度和它们的OPE系数。我们观察到算符谱在3D Ising维处发生了急剧的跃迁，并且发现了强有力的数值证据表明，当一个人接近3D Ising点时，算符从谱中解耦。我们将这一行为与2D中的类似情况进行了比较，在2D中，算子的消失可以用简并的Virasoro表示来理解。
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central chargein the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension, and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.