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

J-Ch. Anglès d'Auriac; Ferenc Iglói

doi:10.1103/physreve.87.022103

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arXiv · 1211.5979

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

J-Ch. Anglès d'Auriac·Ferenc Iglói

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

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J-Ch. Anglès d'Auriac, Ferenc Iglói. 2012-11-26. Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice. https://doi.org/10.1103/physreve.87.022103

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