The $O(2)$ model is a well studied special case of the $O(N)$ model. It also goes by the name “XY model”.
Three of the leading operators in the spectrum: $\phi$ (an $O(2)$ vector), $s$ (a singlet), and $t$ (a symmetric rank-2 tensor i.e. a charge 2 operator) have been determined precisely and rigorously. The scaling dimensions are \[ \Delta_\phi = 0.519088(\mathbf{22}),~\Delta_s = 1.51136(\mathbf{22}),~\Delta_t = 1.23629(\mathbf{11}). \] Four of OPE coefficients between these leading operators have also been determined, albeit not rigorously: \[ \lambda_{\phi\phi s} = 0.687126(27),~\lambda_{s s s} = 0.830914(32),~\lambda_{t t s} = 1.25213(14),~\lambda_{\phi\phi t} = 1.213408(65). \]
Additionally, the flavor current and stress tensor central charges have been determined nonrigorously:
\[ C_J / C_J^{\text {free}}=0.904395(28),~C_T / C_T^{\text {free}}=0.944056(15). \]
Finally, four additional scalar operators: $s'$ (the next-to-leading singlet), $t'$ (the next-to-leading charge 2 operator), and the leading charge 3 and charge 4 operators, have been determined nonrigorously:
\[ \Delta_{s'} = 3.794(8),~\Delta_{t'} = 3.650(2),~\Delta_{3} = 2.1086(3),~\Delta_{4}=3.14(2). \]
These data are from the bootstrap, computed here: https://arxiv.org/pdf/1912.03324.pdf.
Superfluid helium (both He-3 and H-4), apparently.