标题： SO(5)高溫超导体理论中O(5)多临界行为的不稳定性 显示英文标题

标题： Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors

摘要： 我们研究了三维O(3)+O(2)对称朗道-金兹堡-威尔逊理论中的多临界点，该理论描述了两种分别具有O(3)和O(2)对称性的有序参数的竞争。这项研究与SO(5)高Tc超导体理论相关，后者预测了在温度-掺杂相图中存在一个多临界点，在此点反铁磁和超导转变线相交。我们调查了在接近多临界点时，O(3)+O(2)对称性是否有效扩大到O(5)。为此，我们研究了O(5)不动点的稳定性。通过蒙特卡洛模拟，我们表明，O(5)不动点对于自旋-4四次扰动（交叉指数为$\phi_{4,4}=0.180(15)$）是不稳定的，这与最近的场论结果大体一致。这一估计值远大于一阶$\epsilon$-展开估计值$\phi_{4,4}=1/26$，后者常被用于文献中讨论SO(5)理论中的多临界行为。因此，通常不期望在多临界过渡中出现对称扩展。我们还进行了五阶场论重整群流分析，结果显示双临界系统不在稳定解耦不动点的吸引域内。因此，在这些系统中——高温铜氧化物应属于此类——多临界点对应于一级相变。 显示英文摘要

摘要： 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 the 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 the 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 $\phi_{4,4}=0.180(15)$, 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 the 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.