Critical fixed points in class D superconductors

Abstract

We study in detail a critical line on the phase diagram of the Cho-Fisher network model separating three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. This system describes non-interacting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotational invariance. We find that in addition to a tricritical fixed point $W_T$ on that critical line there exist an additional repulsive fixed point $W_N$ (where the vortex disorder concentration $W_N<W_T$), which splits RG flow into opposite directions: toward a clean Ising model at W=0 and toward $W_T$.Comment: 3 pages, one figur

Effective mass and tricritical point for lattice fermions localized by a random mass

“…͑Here we disagree with Refs. 32 and 33, which maintain that the M-I transition exists in graphene as well.͒ Our lattice fermion model is different from the network model 9 used in previous investigations 10,11,15,16 but it falls in the same universality class so we expect the same critical conductivity and critical exponent. For the I-I transition analytical calculations 1,14 give c = G 0 / and = 1, in agreement with our numerics.…”

“…16 The logarithmic scaling ͓Eq. ͑5.1͔͒ of the conductivity in the thermal metal phase, predicted analytically, 1,3 is nicely reproduced by our numerics ͑Fig.…”

“…From the scale dependence of near this tricritical point, we conclude that it is a repulsive fixed point ͑in the sense that scales with increasing L to larger values for ␦M Ͼ ␦M ‫ء‬ and to smaller values for ␦M Ͻ ␦M ‫ء‬ ͒. An attractive tricritical point had been suggested as a possible scenario, 15,16 in combination with a repulsive critical point at some ␦M ‫ءء‬ Ͻ ␦M ‫ء‬ . Our numerics does not support this scenario.…”

“…Earlier numerical investigations 10,11,15,16 of the class BD phase diagram were based on the Cho-Fisher network model. 9 Here we use a staggered-fermion model in the same symmetry class, originally developed in the context of lattice gauge theory 24,25 and recently adapted to the study of transport properties in graphene.…”

Symmetry, Universality and Critical Transitions in the Network Models

“…This scenario was addressed in Ref. [21]. The analysis was performed in the following way: first, for all data points for all system widths, second, without M = 16 data, third, without M = 16,32 data.…”