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Critical behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>โ</mml:mo><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>symmetric models
We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional systems characterized by a matrix order parameter with symmetry $\mathrm{O}(2)\ensuremath{\bigotimes}\mathrm{O}(N)$ and symmetry-breaking pattern $\mathrm{O}(2)\ensuremath{\bigotimes}\mathrm{O}(N)\ensuremath{\rightarrow}\mathrm{O}(2)\ensuremath{\bigotimes}\mathrm{O}(N\ensuremath{-}2)$. Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, โฆ