PMID: 15244888Jul 13, 2004Paper

Disorder-induced rounding of the phase transition in the large-q-state Potts model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M T MercaldoF Iglói

Abstract

The phase transition in the q -state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while it is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional lattices by using the fact that the partition function of the model is dominated by a single diagram of the high-temperature expansion, which is calculated by an efficient combinatorial optimization algorithm. For a given finite sample with discrete randomness the free energy is a piecewise linear function of the temperature, which is rounded after averaging, however, the discontinuity of the internal energy at the transition point (i.e., the latent heat) stays finite even in the thermodynamic limit. For a continuous disorder, instead, the latent heat vanishes. At the phase transition point the dominant diagram percolates and the total magnetic moment is related to the size of the percolating cluster. Its fractal dimension is found d(f) = ( 5 + square root of 5)/4 and it is independent of the type of the lattice and the form of disorder. We argue that the critical behavior is exclusively determined by disorder and the corresponding fixed point is the isotropic version of the so-called inf...Continue Reading

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Citations

Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·László Környei, Ferenc Iglói
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nuno Crokidakis, Paulo Murilo Castro de Oliveira
Jan 14, 2017·Physical Review. E·Jean-Christian Anglès d'Auriac, Ferenc Iglói
Sep 21, 2011·Journal of Physics. Condensed Matter : an Institute of Physics Journal·István A Kovács, Ferenc Iglói
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M KarsaiF Iglói
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dandan HuZohar Nussinov
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M T MercaldoF Iglói
Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe Chatelain
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M KarsaiF Iglói

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