发表机构
School of Physical Sciences, National Institute of Science Education and Research; Homi Bhabha National Institute（物理科学学院，国家科学教育研究中心; 霍米·巴巴国立研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究完全图上无热随机场 Blume-Capel 和 Blume-Emery-Grifitths 模型的 Glauber 动力学相变，通过比较稳态与平衡态，考虑排斥双二次相互作用等，解析推导滞后环形状及方程，揭示相变规律及丰富相图特性。
AI 中文摘要
我们求解了完全图上存在和不存在外部磁场时 Glauber 动力学的两个模型及其平衡态。比较了 Glauber 动力学稳态与平衡态，发现高斯随机场方差 \(R\) 较低时，Glauber 动力学稳态依赖初始状态，超过临界值 \(R_{c}\) 两者重合。\(R\) 类似温度，能精确得到 Glauber 动力学稳态中连续和一阶转变位置。通过考虑 Blume-Emery-Griffiths 模型的排斥双二次相互作用引入挫折。还表明 \(R_c\) 可能为零，且系统初始 \(R_c = 0\) 时，随 \(R\) 增加，在某些耦合区域会转变为随机场 Ising 模型普适性。有均匀磁场时，一阶转变区域在 Glauber 动力学下呈现滞后现象，模型展现多种滞后环形状，我们解析推导了滞后环形状及矫顽场值方程，表明滞后环面积依赖 \(R\)，形状由 \(R = 0\) 时模型行为决定，特别是 Blume-Emery-Griffiths 模型的滞后图有连续和一阶转变区域，产生丰富相图且依赖初始状态。
英文摘要
We solve the two models for Glauber dynamics and in equilibrium, both in the presence and absence of the external magnetic field on a complete graph. We compare the steady state of the Glauber dynamics with equilibrium and find that for low values of variance $R^2$ of the Gaussian random field, the steady state of the Glauber dynamics depends on the initial state. Beyond a critical value $R_{c}$ the equilibrium and non equilibrium steady states coincide. The variance $R$ in random field models behaves similar to the temperature. The location of both the continuous and first order transitions can be obtained exactly for the Glauber dynamics steady state. The frustration is introduced by considering repulsive bi-quadratic interaction for Blume-Emery-Griffiths model. We also consider repulsive bi-quadratic interaction and show that $R_c$ can become zero depending on the value of the crystal field. Interestingly, we also find that even when a system has $R_c=0$ at the start of quasi-static evolution with Glauber dynamics, with increasing $R$, in some regime of the couplings, the model undergoes a crossover to a random field Ising model universality with $R_c$ changing from $0$ to $\sqrt{\frac{2}π}$. In the presence of uniform magnetic field, regions of first order transition exhibit hysteresis under Glauber dynamics. These models exhibit rectangular, hexagonal, parallelogram, wasp-waisted, and double hysteresis loops. We derive the shapes of hysteresis loops analytically and also the equation for the coercive field. We show that while the area under the hysteresis loop depends on $R$, the shape is determined by the behavior of the models at $R=0$. In particular, in the case of Blume-Emery-Griffiths model the hysteresis plots have regions of continuous and first order transitions both, resulting in a rich phase diagram that depends non-trivially on the initial state.
Comments21 pages, 11 figures
