Instability of O(5) multicritical behavior in SO(5) theory of high-Tc superconductors -: art. no. 014532

We study the nature of the multicritical point in the three-dimensional O(3)circle plus 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-T-c 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)circle plus 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 phi(4,4)=0.180(15), in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop epsilon-expansion estimate phi(4,4)=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-T-c cuprates should belong to this class-the multicritical point corresponds to a first-order transition.