平均场近似下非周期相互作用的非普适性态
Non-universal behavior for aperiodic interactions within a mean-field approximation
摘要：
本文研究了平均场极限下Bethe晶格上自旋为1/2的伊辛模型，模型中的相互作用常数遵循两种确定性的非周期序列：Fibonacci序列和倍周期序列.实现了新的序列生成算法，这是获得长序列的基础，因此，精确的结果。我们计算了这两个序列的精确临界温度，以及临界指数$β$，$γ$和$δ$。对于斐波那契数列，指数是经典的，而对于倍周期数列，它们取决于两个交换常数之间的比值。对于倍周期序列，临界指数之间的通常关系在误差条内是满足的。因此，我们表明，平均场的程序可能会导致非经典临界指数。
英文摘要：
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponent $β$, $γ$ and $δ$. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
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