Ultraviolet-Complete Local Field Theory of Persistent Symmetry Breaking in 2+1 Dimensions

Spontaneous symmetry breaking can persist at all temperatures in certain biconical O(N)×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 behavior with good accuracy for all N≥2. We then exhibit the mechanism of discrete symmetry breaking from O(N)×Z_{2}→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 Z_{2} sector. Finally, we determine the critical N above which this phenomenon can be observed to be N_{c}≈15.