An inhomogeneous random recursive lattice was constructed from themulti-branched Husimi square lattice. The number of repeating units connectedon one vertex was randomly set to be 2 or 3 with a quenched ratio $P_2$ or$P_3$ with $P_2+P_3=1$. The model was designed to describe complexthermodynamic systems with variable coordinating neighbors, e.g. thecross-dimensional range around the surface of a bulk materials. Classicalferromagnetic spin-1 Ising model was solved on the lattice to achieve anannealed solution via the local exact calculation technique. The model exhibitsdistinct spontaneous magnetization similar to the deterministic system, withhowever rigorous thermal fluctuations and significant singularities on theentropy behavior around the critical temperature, indicating a complexsuperheating and supercooling frustration in the cross-dimensional rangeinduced by the stochasticity. The critical temperature was found to beexponentially correlated to the structural ratio $P$ with the coefficientfitted as 0.53187, while the ground state energy presents linear relation to$P$, implying a well-defined average property according to the structuralratio.
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机译：由多分支Husimi方格构造了一个不均匀的随机递归格。一个顶点上连接的重复单元的数量随机设置为2或3，其中淬灭比为$ P_2 $或$ P_3 $，其中$ P_2 + P_3 = 1 $。该模型旨在描述具有可变协调邻居的复杂热力学系统，例如散装材料表面周围的尺寸范围。通过局部精确计算技术，在晶格上求解了经典铁磁自旋1 Ising模型，以实现退火解决方案。该模型表现出与确定性系统相似的明显自发磁化强度，但是在临界温度附近存在严格的热涨落和熵行为的显着奇异点，这表明由随机性引起的跨维度范围内的复杂的过热和过冷挫折。发现临界温度与结构比$ P $呈指数相关，系数拟合为0.53187，而基态能量与$ P $呈线性关系，意味着根据结构比具有明确定义的平均特性。
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