Critical behavior of coupled q -state Potts models under weak disorder

Abstract

We investigate the effect of weak disorder on different coupled q-state Potts models with q ≤ 4 using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered q 1 × q 2 -state Potts model and the two disordered q 1 , q 2 -state Potts models (q 1 = q 2 ), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two q-state Potts models are considered (q > 2), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.

Coupled Ising models with disorder

“…Another non trivial fixed point at ∆ * > 0 cannot a priori be excluded but is very unprobable according to the symmetries of the model under consideration. Note that contrary to the examples treated in [8,9,10] where some infinitesimal disorder changes the weakly driven first order transition into a continuous one, here a finite value of the disorder is needed! …”

“…The addition of weak bond randomness, even infinitesimal, makes the system flow to N decoupled critical Ising models [8]. This result has been extended to the case of N coupled Potts models [9,10]. The result was a non-Ising like second order transition, the universality class depending on the sign of the coupling between the models.…”