Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron

The observation of hysteresis effects in single molecule magnets like Mn$_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T=0 this system undergoes a first order metamagnetic phase transition at a critical field $\Bcrit$ between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.