标题： 2+1 维中持久对称性破缺的完备局部场论 显示英文标题

标题： UV complete local field theory of persistent symmetry breaking in 2+1 dimensions

摘要： 自发对称性破缺在某些双锥形$\mathrm{O}(N)\times \mathbb{Z}_2$向量模型中可以在所有温度下持续存在，当底层场论是紫外完备的时候。到目前为止，这类理论的存在性已在分数维度中得到证实，适用于局部但非幺正的模型，或在 2+1 维度中但针对非局部模型。在这里，我们直接在 2+1 维度中采用泛函方法研究零温与有限温度下的局部模型。在零温情况下，我们确立了我们的方法对于所有$N\geq 2$都能高精度地描述量子临界行为。然后，我们展示了当$N$为有限但较大的值时，在双锥临界点附近随着温度升高从$\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$出发的离散对称性破缺机制。我们计算了相应的有限温度相图，并进一步表明在此方法中完全遵守 Hohenberg-Mermin-Wagner 定理，即对称性破缺仅发生在$\mathbb{Z}_2$分量中。最后，我们确定了临界$N$，在此之上可以观察到这种现象，其值为$N_c \approx 15$。 显示英文摘要

摘要： Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$.