Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice

Abstract

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 $d_{\mathrm{eff}}>2$. 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.

7 pages 6 figures

References in corpus (4)

• Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption
• Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study
• Critical Behavior of Three-Dimensional Disordered Potts Models with Many States
• Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit

Cited by in corpus (3)

• Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
• Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
• Dynamical barriers of pure and random ferromagnetic Ising models on fractal lattices