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The critical behavior of the three-dimensional $N$-vector chiral model isstudied for arbitrary $N$. The known six-loop renormalization-group (RG)expansions are resummed using the Borel transformation combined with theconformal mapping and Pad\'e approximant techniques. Analyzing the fixed pointlocation and the structure of RG flows, it is found that two marginal values of$N$ exist which separate domains of continuous chiral phase transitions $N >N_{c1}$ and $N < N_{c2}$ from the region $N_{c1} > N > N_{c2}$ where suchtransitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and$N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical tothat given by the $\epsilon$ and 1/N expansions with the chiral fixed pointbeing a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be afocus having no generic relation to the stable fixed point seen at small$\epsilon$ and large $N$. In this domain, containing the physical values $N =2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-likemanner giving rise to unusual crossover regimes which may imitate varying(scattered) critical exponents seen in numerous physical and computerexperiments.Comment: 12 pages, 3 figure

physical review. b, condensed matter

Critical thermodynamics of a three-dimensional chiral model for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>&gt;</mml:mo><mml:mn /><mml:mn>3</mml:mn><mml:mn /></mml:math>

Critical thermodynamics of a three-dimensional chiral model forN>3