Two-parameter scaling theory of transport near a spectral node

We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-parameter scaling flow toward a finite fixed point. The latter is the minimal conductivity of the infinite system. Depending on boundary conditions, we also observe unstable fixed points with conductivities much larger than the experimentally observed values, which may account for results found in some numerical simulations. By including a spectral gap we extend our scaling approach to describe a metal-insulator transition.Comment: 4.5 pages, 4 figures, published versio

Interplay of topology and geometry in frustrated 2d Heisenberg magnets

We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a phase transition which separates a low temperature, spin-wave dominated regime from a high temperature regime where defects are abundant. Our approach can account for the crossover qualitatively and both the temperature dependence of the correlation length as well as a broad but well defined peak in the specific heat are reproduced. We find no signatures of a finite temperature transition and an accompanying diverging length scale. Our analysis is consistent with a rapid crossover driven by topological defects.Comment: 12 pages, 8 figures, final version to appear in Physical Review

Quantum Hall effect induced by electron-phonon interaction

When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are many-body states commensurate to Haldane's staggered flux model or to lattice models with periodically modulated strain. We find that the effective field theories of these phases exhibit characteristic Chern-Simons terms, whose coefficients are related to the topological invariants of the microscopic model. This implies that the corresponding quantized Hall conductivities characterize these insulating states.Comment: Accepted for publishing with Annals of Physics on April 30th, 202

Renormalized transport properties of randomly gapped 2D Dirac fermions

We investigate the scaling properties of the recently acquired fermionic non--linear $\sigma$--model which controls gapless diffusive modes in a two--dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a novel renormalizable nonlocal field theory. For zero mean random gap, it is characterized by the absence of a dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.Comment: Version published with minor change

Discourse, agency, and social license to operate in New Zealand's marine economy

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Optical conductivity of graphene in the presence of random lattice deformations

We study the influence of lattice deformations on the optical conductivity of a two-dimensional electron gas. Lattice deformations are taken into account by introducing a non-abelian gauge field into the Eucledian action of two-dimensional Dirac electrons. This is in analogy to the introduction of the gravitation in the four-dimensional quantum field theory. We examine the effect of these deformations on the averaged optical conductivity. Within the perturbative theory up to second order we show that corrections of the conductivity due to the deformations cancel each other exactly. We argue that these corrections vanish to any order in perturbative expansion.Comment: 9 pages, 9 figure

Dissecting the Discourse of Social Licence to Operate

The term “social licence to operate”, or SLO, has increasingly featured in public discussion about commercial operations in the marine environment. As part of the Sustainable Seas National Challenge, we are studying how this term is being used in New Zealand and its implications for industry-community relations

Efficiency = Equity and Other Musings on Economics and Sustainable Development

Conventional wisdom says that equity concerns are beyond the scope of economic analysis and that achieving equity objectives will often come at a cost in terms of efficiency. Examination of the underlying meaning of efficiency and how it is defined, however, reveals that this tension between efficiency and equity is more apparent than real. The paper also explores the application of other economic concepts to the field of sustainable development, including the use of discounting for present value, Gross Domestic Product as a measure of well-being, and rational utility maximisation vs. bounded rationality as models of human behaviour.Agricultural and Food Policy, Community/Rural/Urban Development, Environmental Economics and Policy, Land Economics/Use, Research Methods/ Statistical Methods,