Replica symmetry breaking in the RKKY skyrmion crystal system

We study the RKKY Heisenberg model on a three-dimensional stacked-triangular lattice under magnetic fields by extensive Monte Carlo simulations to get insight into chiral-degenerate symmetric skyrmion crystal (SkX) in centrosymmetric metallic magnets. The triple-$q$ SkX state and double-$q$ states are realized, together with single-$q$ state. find an unexpected phenomenon of replica-symmetry breaking (RSB) well-known glassy systems, although Hamiltonian ordered entirely regular. In RSB phase, macroscopically coexists state, spite fact that these cannot be transformed via any Hamiltonian-symmetry operation. thermodynamic limit, free energies degenerate whereas free-energy barrier between diverges, ergodicity. A similar is observed also phase where Experimental implications discussed.