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

d'Auriac, JCA and Iglói, Ferenc (2013) Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS (2001-2015), 87 (2). ISSN 1539-3755

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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 deff > 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 selfsimilar, it is well represented 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.

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