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o3_model [2021/04/27 20:24]
Scott Lawrence [Operator content] 		o3_model [2023/01/30 03:02] (current)
Rajeev S. Erramilli
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 ===== Operator content ===== ===== Operator content =====
  
-There are two relevant operators, $\phi$ (an $O(3)$ vector) and $s$ (a singlet). The scaling dimensions are+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
 \[ \[
-\Delta_\phi = 0.51928(62) \text{ and } \Delta_s = 1.5957(55)+\Delta_\phi = 0.518936(\mathbf{67}),~\Delta_s = 1.59488(\mathbf{81}),~\Delta_t = 1.20954(\mathbf{32}).
 \] \]
-while the nonvanishing OPE coefficients are+ 
 +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:
 \[ \[
-\lambda_{sss} = 0.499(12) \text{ and } \lambda_{\phi\phi s} = 0.5244(11) +C_J / C_J^{\text {free}}= 0.90632(16),~C_T / C_T^{\text {free}}= 0.944524(28).
-\text.+
 \] \]
  
-These data are from the bootstrap, computed here: [[https://arxiv.org/pdf/1603.04436.pdf]].+These data are from the bootstrap, computed here: [[https://arxiv.org/pdf/2011.14647.pdf]].
 ===== External links ===== ===== External links =====
  
   * [[https://en.wikipedia.org/wiki/Classical_Heisenberg_model|Wikipedia]]   * [[https://en.wikipedia.org/wiki/Classical_Heisenberg_model|Wikipedia]]
Last modified: 2021/04/27 20:24
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