Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

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The fixed point that governs the critical behavior of magnets described by the N-vector chiral model under the physical values of N (N =2, 3) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.