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--- o3_model [2021/04/10 06:07]
Scott Lawrence created
+++ o3_model [2023/01/30 03:02] (current)
Rajeev S. Erramilli
@@ Line 2: / Line 2: @@
 {{tag>3d}}
+The $N=3$ special case of the [[on_model]] also goes by the name "Heisenberg model".
+===== Operator content =====
+Three of the leading operators in the spectrum have had their dimensions precisely determined: $\phi$ (an $O(3)$ vector), $s$ (a singlet), and $t$ (a symmetric rank-2 tensor). The scaling dimensions are
+\[
+\Delta_\phi = 0.518936(\mathbf{67}),~\Delta_s = 1.59488(\mathbf{81}),~\Delta_t = 1.20954(\mathbf{32}).
+\]
+Additionally, the rank-4 tensor $t_4$ has a rigorous upper bound for its scaling dimension:
+\[
+\Delta_{t_4} < 2.99056.
+\]
+Notably, this result makes this operator relevant.
+Five of OPE coefficients have also been determined, albeit not rigorously:
+\[
+\lambda_{\phi\phi s} =0.524261(59),~\lambda_{s s s} = 0.5055(11),\\~\lambda_{t t s} = 0.98348(39),~\lambda_{\phi\phi t} = 0.87451(22),~\lambda_{t t t} = 1.49957(49).
+\]
+The flavor current and stress tensor central charges have been determined nonrigorously:
+\[
+C_J / C_J^{\text {free}}= 0.90632(16),~C_T / C_T^{\text {free}}= 0.944524(28).
+\]
+These data are from the bootstrap, computed here: [[https://arxiv.org/pdf/2011.14647.pdf]].
+===== External links =====
+  * [[https://en.wikipedia.org/wiki/Classical_Heisenberg_model|Wikipedia]]

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