Spin Glass State and Other Magnetic Structures with Their Symmetries in Terms of the Fibre Bundle Approach

Abstract

The fibre bundle approach has been applied to derive the explicit formulas presenting all the eight fundamental magnetic structures and their symmetry groups including the spin glass state. The explanation of the uniqueness of the spin glass state has its roots in the appearance of the probability function p(i, j) in the second term of the assumed Hamiltonian. This term actually describes the random distribution of either dopants or defects in the ferromagnetic matrix under the percolation threshold. On this basis the Gaussian type randomness was derived for both the general global magnetic coupling constant and the magnetization vector, the latter effect bringing to the statistical features of the magnetic structure and the magnetic symmetry group of the spin glass state.