Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$

Details Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$ Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$

2005-11-08

arxiv.org/abs/cond-mat/0511203v1

Phys. Rev. E73, 026126 (2006)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 11 figures

Scientific paper

10.1103/PhysRevE.73.026126

We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\delta>\delta_t$ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that $\delta_t$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as $\beta_t/\nu_t=0.10(2)$ and $\nu_t=0.67(4)$. We claim these exponents are $q$ independent, for sufficiently large $q$. In the second-order transition regime the critical exponents $\beta_t/\nu_t=0.60(2)$ and $\nu_t=0.73(1)$ are independent of the strength of disorder.

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