Isolated Weyl cones in a disordered environment do not show the phenomenon of Anderson localization due to the abscence of backscattering processes. However, besides the conventional three dimensional diffusive metal, an additional semimetallic phase can form. In this paper we study the effect of tilt on the physics of disorder in isolated Weyl cones. Our main finding is that while the semimetallic phase remains a stable phase, tilt decreases the size of the semimetallic region. Conversely, disorder increases the effective tilt of the quasiparticle excitations.

We study the effects of disorder and Coulomb interactions on the physics of three-dimensional type-I Weyl fermions with tilted and anisotropic dispersions in a renormalization group approach. To lowest non-trivial loop order we show that the tendency of the Coulomb interactions to restore the symmetry of the dispersion in the semimetallic region of the phase diagram dominates the stabilization of the tilt and anisotropy favored by weak disorder. We argue that the topology of the renormalization flow of the disorder and Coulomb couplings is essentially determined by gauge invariance, so that these findings continue to hold qualitatively at any order in perturbation theory.

The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter-and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out of the fully polarized phase into the macro-spin liquid displaying quantum criticality typical for 2d quantum systems.Introduction: Geometrical frustration in magnetic systems can give rise to a multitude of exotic classical and quantum phases. An analysis of the classical limit often reveals a large degeneracy in the ground-state manifold, which can be lifted by quantum or thermal fluctuations thereby selecting an ordered state. This phenomenon is conventionally referred to as 'order by disorder'. A more exotic version of degeneracy lifting is called 'disorder by disorder' [1-5]: out of multiple classical ground states a disordered state is selected. Paradigmatic examples for either of the two phenomena can be found in two dimensions for the transverse field Ising model (TFIM), on the triangular and the Kagomé lattices, respectively. In both cases a polarized phase is found at high transverse fields. On the triangular lattice an infinitesimal transverse field is sufficient to select an ordered state out of the degenerate classical manifold, thereby providing an example of order by disorder. The selected state is the so-called √ 3 × √ 3-state which maximizes the number of flippable spins. The two phases are connected via a second order phase transition in the 3d XY universality class [1,4,6]. In contrast, in the case of the Kagomé lattice any finite transverse field selects the disordered polarized phase which does not break any symmetry, providing an example of disorder by disorder [1,4].Recently, it was found that interesting effects of frustrated magnetism can also be encountered in the threedimensional swedenborgite systems. For example, classical O(3) Heisenberg spins on this lattice exhibit a wide spin liquid regime for a certain parameter and temperature range and can undergo a fluctuation driven order by disorder transition to a nematic phase at very low temperatures [7]. It was also shown that the classical Ising model with and without longitudinal magnetic field boasts different phases with extensive and subextensive ground-state degeneracy [8]. Depending on system parameters, the swedenborgite structure corresponds to either a stack of weakly coupled Kagomé layers or an emergent triangular lattice of stiff macro-spins. As a result, one can speculate that the order by disorder of the triangular lattice TFIM and the disorder by disorder of the

Magnetically frustrated systems provide fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles is yet to be found. Using measurements on single crystals of Ho2Ir2O7 combined with dipolar Monte Carlo simulations, we show that the isothermal magnetoresistance is highly sensitive to the monopole density. Moreover, we uncover an unexpected and strong coupling between the monopoles on the holmium sublattice and the antiferromagnetically ordered iridium ions. These results pave the way towards a quantitative experimental measure of monopole density and demonstrate the ability to control antiferromagnetic domain walls using a uniform external magnetic field, a key goal in the design of next-generation spintronic devices.