Nonlocal field correlators on the lattice in HP$^1$ $\sigma$-model

Connected two-point field strength correlators have been measured on the lattice in quaternionic projective $\sigma$-model of pure $SU(2)$ Yang-Mills theory. The correlation lengths, extracted from the exponential fit for these correlators, are found to be $\lambda_1^{-1}=1.40(3)$ GeV and $\lambda^{-1}=1.51(3)$ GeV in good agreement with other existing calculations. The dependence of bilocal functions on the connector shape was studied.