text: I.  INTRODUCTION 
  
  frustrated magnetic 
  systems1 still raises great interest, both in consequence 
  of theoretical aspects, related to their peculiar criti- 
  cal properties2, and in view of possible technological 
  applications3. Indeed, beside conventional ferromagnetic 
  or antiferromagnetic phase transitions, in many new ma- 
  terials other nontrivial and unconventional forms of or- 
  dering have been observed4,5. A quantity of particular 
  interest in this context is the spin chirality, an order pa- 
  rameter which turned out to be extremely relevant in, 
  e.g., magnetoelectric materials6, itinerant MnSi7, binary 
  compounds as FeGe8, glass transition of spins9, and XY 
  helimagnets, as Holmium, Terbium or Dysprosium10. In 
  the latter case, a new universality class was predicted be- 
  cause a Z2 × SO(2) symmetry is spontaneously broken 
  in the ordered phase2: In fact, when dealing with such 
  systems, in addition to the SO(2) symmetry of the spin 
  degrees of freedom ~Si, one has to consider also the Z2 
  symmetry of the spin chirality κij ∝ 
  
  The study of  low dimensional 