Instability of O(5) multicritical behavior in SO(5) theory of high-Tc superconductors - Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore (Physical review. B, Condensed matter and materials physics, 2005)
We study the nature of the multicritical point in the three-dimensional O(3)⊕O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for SO(5) theory of high-Tc superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet. We investigate whether O(3)⊕O(2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent ϕ4,4=0.180(15), in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop ϵ-expansion estimate ϕ4,4=1/26, which has often been used in the literature to discuss the multicritical behavior within SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition. We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems—high-Tc cuprates should belong to this class—the multicritical point corresponds to a first-order transition.
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