title: Instability of the mean-field states and generalization of phase separation in long-range interacting systems.
abstract: Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et al. [Phys. Rev. B 61, 11521 (2000)] that the mean-field theory is exact for spin systems with nonadditive long-range interactions. This is called "exactness of the mean-field theory." We show that the exactness of the mean-field theory holds for systems on a lattice with nonadditive two-body long-range interactions in the canonical ensemble with unfixed order parameters. We also show that in a canonical ensemble with fixed order parameters, exactness of the mean-field theory does not hold in one parameter region, which we call the "non-mean-field region." In the non-mean-field region, an inhomogeneous configuration appears, in contrast to the uniform configuration in the region where the mean-field theory holds. This inhomogeneous configuration is not the one given by the standard phase separation. Therefore, the mean-field picture is not adequate to describe these states. We discuss phase transitions between the mean-field region and the non-mean-field region. Exactness of the mean-field theory in spin glasses is also discussed.
authors: Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan. mori@spin.phys.s.u-tokyo.ac.jp
authors: Takashi
authors: T
authors: Mori