The infinite-ranged spin glass with m-component spins

Abstract

The Sherrington-Kirkpatrick model (1978) of an Ising spin glass is generalised to the case of m-component spins. The authors have studied the stability of the solution which preserves the symmetry between replica systems and found that although the solution is stable at high temperatures, it presents an instability in the spin glass phase for any finite m. It is found that in the limit m to infinity the m-component system yields the same free energy as that obtaining for the Berlin and Kac spherical model (1952) of a spin glass and this solution turns out to be the only stable one in the m to infinity limit.