In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of $\mathrm{O}(N)$ field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of $2N-3$ Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions $d<4$ they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for $N=2$, and a generalization for arbitrary $N$, which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an $xy$ magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.

中文翻译：

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非平衡 O(N) 模型临界异常点的普遍现象学


在热平衡中，相变的动力学很大程度上受波动耗散关系控制：一方面，摩擦抑制波动，而另一方面，热噪声与摩擦常数成正比。一旦失去平衡，这种平衡就会消失，并且在有限噪声水平的情况下，可能会出现摩擦因抗阻尼而消失的情况。我们研究了一系列 $\mathrm{O}(N)$ 场论，其中这种情况是在相变时实现的，我们将其视为关键的例外点。在有序阶段，抗阻尼会导致有序参数的连续极限环旋转，并增加 $2N-3$ Goldstone 模式的数量。然而，在接近临界异常点时，由于摩擦的抑制，波动发散如此强烈，以至于在维度 $d<4$ 中，它们普遍要么破坏预先存在的静态秩序，要么引起波动引起的一阶转变。这通过 $N=2$ 的 Dyson-Schwinger 方程的环路校正的完整恢复以及任意 $N$ 的泛化得到了证明，可以在长波长限制中求解。我们证明，为了实现这种物理现象，没有必要使系统远离平衡：利用戈德斯通模式的特殊保护，从 $xy$ 磁体到亚铁磁体的转变受到特殊的控制临界点一旦受到微弱扰动就会偏离热平衡。