Reflection symmetry in mean-field replica-symmetric spin glasses
  The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica symmetric mean field approximation. If in the pure system the transition to the ordered phase is of the second order, then in the corresponding random system the glass regime appears as a result of a phase transition; if the transition in the pure system is of the first order, then glass and ordered regimes grow continuously in the random system on cooling. 
N. V. Gribova, V. N. Ryzhov, T. I. Schelkacheva, E. E. Tareyeva