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Competing orders, competing anisotropies, and multicriticality: The case of Co-doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">YbRh</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Si</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
Motivated by the unusual evolution of magnetic phases in stoichiometric and Co-doped ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$, we study Heisenberg models with competing ferromagnetic and antiferromagnetic ordering combined with competing anisotropies in exchange interactions and $g$ factors. Utilizing large-scale classical Monte Carlo simulations, we analyze the ingredients required to obtain the characteristic crossing point …