Nonintegrability of (2+1)(2+1)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis

While many integrable spin systems are known to exist in 1+11+1 and 2+12+1 dimensions, the integrability property of the physically important (2+12+1)-dimensional isotropic Heisenberg ferromagnetic spin system in the continuum limit has not been investigated in the literature. In this Letter, we show through a careful singularity structure analysis of the underlying nonlinear evolution equation that the system admits logarithmic type singular manifolds and so is of non-Painlevé type and is expected to be nonintegrable.