We study the magnetic phases of a non-equilibrium spin chain, where coherent interactions between neighboring lattice sites compete with alternating gain and loss processes. This competition between coherent and incoherent dynamics induces transitions between magnetically aligned and highly mixed phases, across which the system changes from a low- to an effective infinite-temperature state. We show that the origin of these transitions can be traced back to the dynamical effect of parity-time-reversal symmetry breaking, which has no counterpart in the theory of equilibrium phase transitions. This mechanism also results in very atypical features and we find first-order transitions without phase co-existence and mixed-order transitions which do not break the underlying $U(1)$ symmetry, even in the appropriate thermodynamic limit. Thus, despite its simplicity, the current model considerably extends the phenomenology of non-equilibrium phase transitions beyond that commonly assumed for driven-dissipative spins and related systems.

中文翻译：

---

自旋晶格中具有增益和损耗的非平衡磁相

我们研究了非平衡自旋链的磁相，其中相邻晶格位点之间的相干相互作用与交替的增益和损耗过程竞争。相干动力学和非相干动力学之间的竞争导致了磁性排列相和高度混合相之间的跃迁，整个系统从低相转变为有效的无限温度状态。我们表明，这些跃迁的起源可以追溯到奇偶-时间-逆对称分裂的动力学效应，这在平衡相变理论中是没有对立的。这种机制还导致非常不典型的特征，我们发现没有相共存的一阶跃迁和混合阶跃迁都不会破坏基础$ü（\mathrm{1个}）$即使在适当的热力学极限内也可以保持对称。因此，尽管模型简单，但当前模型大大扩展了非平衡相变的现象学，超出了驱动耗散自旋和相关系统的一般假设。