Locally self-similar phase diagram of the disordered Potts model on the   hierarchical lattice
  We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality $d_{\rm eff} > 2$. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase-boundary in the vicinity of the multicritical point is self-similar, it is well represent ed by a logarithmic spiral. We expect infinite number of reentrances in the thermodynamic limit, consequently one can not define standard thermodynamic phases in this region. 
J-Ch. Angl\`es d'Auriac and Ferenc Igl\'oi
cond-mat.stat-mech cond-mat.dis-nn