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We consider a 1+3 dimensional spin system. The spin-wave (magnon) field isdescribed by the O(3) non-linear sigma model with a symmetry-breakingpotential. This interacts with a slow spin SU(2) doublet Schrodinger fermion.The interaction is described by a generalized nonperturbative Yukawa coupling,and the self-consistency condition is solved with the aid of a non-relativisticGribov equation. When the Yukawa coupling is sufficiently strong, the solutionexhibits supercriticality and soft confinement, in a way that is quiteanalogous to Gribov's light-quark confinement theory.  The solution corresponds to a new type of spin polaron, whose condensationmay lead to exotic superconductivity.

Soft confinement in a 3-d spin system