最短轨道凝聚模型的相变

PHASE TRANSITION OF THE SHORTEST—PATH AGGREGATION

应用重整化群计算最短轨道模型的生长几率分布｛Ｐα，ｉ｝及其构型权重Ｃα（２×２原胞和３×３原胞），从而得出多分形热力学的配分函数Ｚ（ｑ，Ｌ），自由能Ｆ（ｑ，Ｌ），能量Ｅ（ｑ，Ｌ），比热ｃ（ｑ，Ｌ）和广义维数Ｄｑ，结果表明该模型在ｑ＝ｑｃ≈０处发生相变，即当ｑ＜ｑｃ时，生长几率分布｛Ｐα，ｉ｝不具有多分形性质。

The growth probabilities {Pα,i} and configuration weights Cα (for 2×2 cell and 3×3 cell) are obtained by using the renormalizationgroup method. The “partition function” Z(q,L), “Free energy”F(q,L),“energy” E(q,L),“specific heat”c(q,L) and hierarchical dimensions Dq are calculated. The evidence has been found for suggesting the existence of phase transition in the multifractal spectrum of the SPA model and position of critical point qc=0. In the words, the distribution of growth probability has no multifractal features.