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We propose and investigate numerically a one-dimensional model which exhibitsa non-Anderson disorder-driven transition. Such transitions have recently beenattracting a great deal of attention in the context of Weyl semimetals,one-dimensional systems with long-range hopping and high-dimensionalsemiconductors. Our model hosts quasiparticles with the dispersion $\pm|k|^\alpha \mathrm{sign} k$ with $\alpha<1/2$ near two points (nodes) inmomentum space and includes short-range-correlated random potential whichallows for scattering between the nodes and near each node. In contrast withthe previously studied models in dimensions $d<3$, the model considered hereexhibits a critical scaling of the Thouless conductance which allows for {anaccurate} determination of the critical properties of the non-Andersontransition, with a precision significantly exceeding the results obtained fromthe critical scaling of the density of states, usually simulated at suchtransitions. We find that in the limit of the vanishing parameter$\varepsilon=2\alpha-1$ the correlation-length exponent$\nu=2/(3|\varepsilon|)$ at the transition is inconsistent with the prediction$\nu_{RG}=1/|\varepsilon|$ of the perturbative renormalisation-group analysis.Our results allow for a numerical verification of the convergence of$\varepsilon$-expansions for non-Anderson disorder-driven transitions and, ingeneral, interacting field theories near critical dimensions.

Non-Anderson critical scaling of the Thouless conductance in 1D