Nonintegrability of [formula omitted]-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis

Abstract

While many integrable spin systems are known to exist in 1 + 1 and 2 + 1 dimensions, the integrability property of the physically important ( 2 + 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.