论文标题
与$ p $ -spin互动的完全连接的ISING模型中的耗散相变
Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
论文作者
论文摘要
在本文中，我们研究了$ p \ geq 2 $的驱动驱动性P-Spin模型。在热力学极限中，运动方程是通过使用半经典方法得出的。长期渐近状态是通过分析获得的，在参数空间的某些区域中表现出多稳定性。稳态是独一无二的，因为旋转的数量是有限的。但是稳态磁化的热力学极限显示出半经典多稳定区域内的非分析行为。我们发现一阶和连续的耗散相变。随着旋转的数量的增加，根据连续过渡时的功率定律，Liouvillian间隙和磁化方差都消失了。在一阶过渡时，差距指数伴随着热力学极限的磁化突变。过渡的属性取决于对称性和半经典多构性，在$ p = 2 $，奇数$ p $（$ p \ geq 3 $）中，甚至$ p $（$ p \ geq 4 $）之间在质量上有所不同。
In this paper, we study the driven-dissipative p-spin models for $p\geq 2$. In thermodynamics limit, the equation of motion is derived by using a semiclassical approach. The long-time asymptotic states are obtained analytically, which exhibit multi-stability in some regions of the parameter space. The steady state is unique as the number of spins is finite. But the thermodynamic limit of the steady-state magnetization displays nonanalytic behavior somewhere inside the semiclassical multi-stable region. We find both the first-order and continuous dissipative phase transitions. As the number of spins increases, both the Liouvillian gap and magnetization variance vanish according to a power law at the continuous transition. At the first-order transition, the gap vanishes exponentially accompanied by a jump of magnetization in thermodynamic limit. The properties of transitions depend on the symmetry and semiclassical multistability, being qualitatively different among $p=2$, odd $p$ ($p\geq 3$) and even $p$ ($p\geq 4$).
