Title: Giant effective $g$-factor due to spin bifurcations in polariton condensates

Abstract: We predict giant susceptibility of spin-bifurcating polariton condensates to externally applied permanent magnetic field. In the presence of spin-anisotropic polariton-polariton interactions, the condensate spontaneously takes an elliptically polarised state, {whose perturbation dynamics can be interpreted in terms of the presence of strong effective magnetic field} significantly surpassing the external one. Surprisingly, this behaviour of the addressed strongly out-of-equilibrium system in the vicinity of a critical point exhibits intriguing analogy with the second-order phase transition. The predicted field-enhancement effect can be utilized for creation of topologically nontrivial states of Bogoliubov's excitations existing on top of the polariton condensate.