理解无序系统中的跳跃不连续性
Understanding jump discontinuity in disordered system
AI总结：
研究无序系统中外部场作用下磁化率的跳跃不连续性，通过Ising模型分析不同协调数站点的磁化曲线，揭示跳跃来源及临界点识别方法。
摘要：
复杂系统对缓慢变化的外部力的响应通常在临界点附近表现出序参量的跳跃不连续性。然而，这种不连续性通常分解为更小的跳跃，使仅通过模拟难以确定临界点。本文通过经典Ising模型在外场h下的迟滞响应，研究非平衡零温随机场Ising模型在稀疏系统中的跳跃断裂现象。考虑协调数z=4的Bethe晶格，稀释比例(1-c)后，晶格包含不同协调数的站点。获得整个晶格及各子晶格的磁化曲线精确解，发现总磁化不连续性由不同协调数站点的跳跃叠加产生，发生在相同外部场h_cri处。主导贡献来自高浓度和高协调数的站点，但触发大跳跃的站点多为z≥3。此外，通过立方晶格测试，其中无精确结果。本文分析有助于理解数值模拟和实验中的跳跃波动。
英文摘要：
The response of a complex system to a slow varying external force often displays a jump discontinuity in the order parameter near the critical point. However, this discontinuity is not usually a single jump but rather breaks into smaller jumps which makes it difficult to locate the critical point on approaching its vicinity based only on simulations, in the absence of exact results. Our work is a small effort in understanding these breaks in jump through the hysteretic response of a classical Ising spin system to an external field, $h$, in the context of a nonequilibrium zero-temperature random field Ising model on dilute systems. We consider a Bethe lattice with coordination number, $z = 4$, and dilute a fraction $(1-c)$ of the sites. Therefore the lattice now consists of sites with varying $z = 4, 3, 2, 1$ and possibly few isolated sites $(z=0)$, depending on the concentration $c$. We obtain the exact solution of the magnetization curve, $m(h)$ vs $h$, for the entire lattice as well as for each sublattice of different $z$ coordinated sites, $m_4(h), m_3(h), m_2(h), m_1(h), m_0(h)$. The discontinuity in total magnetization is the result of the superposition of the jumps of different $z$ coordinated sites and observed at the same value of external field, $h_{crit}$. The dominant contribution to the jump comes from those sites with higher concentration and larger $z$. However, the triggering sites responsible for large jumps are mostly $z\ge3$. We test this on cubic lattices as well, where exact results are not available. We hope our analysis will help in understanding fluctuations around a jump in numerical simulations as well as experiments.
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