Phase-transitions of the random bond Potts chain with long-range interactions

Abstract

We study phase-transitions of the ferromagnetic $q$-state Potts chain with random nearest-neighbour couplings having a variance ${\Delta }^2$ and with homogeneous long-range interactions, which decay with the distance as a power $r^{-(1+\sigma )}$, $\sigma >0$. In the large-$q$ limit the free-energy of random samples of length $L\le 2048$ is calculated exactly by a combinatorial optimization algorithm. The phase-transition stays first-order for $\sigma <{\sigma }_c(\Delta )\le 0.5$, while the correlation length becomes divergent at the transition point for ${\sigma }_c(\Delta )<\sigma <1$. In the latter regime the average magnetization is continuous for small enough $\Delta$, but for larger $\Delta$ it is discontinuous at the transition point, thus the phase-transition is of mixed order.

9 pages 13 figures

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