Bicritical phenomena and scaling properties of O(5) model

The competition between two orders which have three and two components, respectively, in three dimensions, modeling the general phase diagram of high-Tc superconductivity (SC) with proximity of antiferromagnetism (AF) and d-wave SC, is investigated by Monte Carlo simulations on an O(5) Hamiltonian and a scaling theory. It is shown that the bicritical point is stable to biquadratic perturbations of AF–SC repulsions, while the biconical, tetracritical point takes the place for attractive, biquadratic AF–SC interactions, in contrast to the ε expansions of the renormalization group. The bicritical scaling theory formulated on the order parameters provides a powerful tool for deriving precise estimates of the bicritical point and the bicritical and crossover exponents.