We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a phase with spontaneous temporal oscillations of the magnetization, on top of the usual paramagnetic and ferromagnetic phases. This behavior is obtained by introducing dynamic field variables coupled to the spins through nonreciprocal couplings. We determine a nonequilibrium generalization of the Landau free energy in terms of the large deviation function of the magnetization and of an appropriately defined smoothed stochastic time derivative of the magnetization. While the transition between paramagnetic and oscillating phase is continuous, the transition between ferromagnetic and oscillating phases is found to be discontinuous, with a coexistence of both phases, one being stable and the other one metastable. Depending on parameter values, the ferromagnetic points may either be inside or outside the limit cycle, leading to different transition scenarios. The stability of these steady states is determined from the large deviation function. We also show that in the coexistence region, the entropy production has a pronounced maximum as a function of system size.

中文翻译：

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非平衡平均场自旋模型中从铁磁态到振荡态的不连续相变

我们研究了一个非平衡铁磁平均场自旋模型，该模型在通常的顺磁和铁磁相之上表现出具有磁化强度自发时间振荡的相。这种行为是通过引入通过不可逆耦合耦合到自旋的动态场变量来获得的。我们根据磁化强度的大偏差函数和适当定义的磁化强度的平滑随机时间导数确定朗道自由能的非平衡概括。虽然顺磁相和振荡相之间的转变是连续的，但铁磁相和振荡相之间的转变被发现是不连续的，两种相共存，一种是稳定的，另一种是亚稳定的。根据参数值，铁磁点可能位于极限环内部或外部，从而导致不同的转变情况。这些稳态的稳定性是由大偏差函数决定的。我们还表明，在共存区域，熵产生作为系统尺寸的函数具有明显的最大值。