Nobre FD, Curado EM
Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario, Caixa Postal 1641, 59072-970 Natal, Rio Grande do Norte, Brazil.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt A):4597-605. doi: 10.1103/physreve.62.4597.
The extensive ground-state entropy of frustrated systems on fractal lattices is investigated. Two methods of calculation are proposed, namely, recursive and factorization approaches. In the recursive approach the calculation is based on exact recursion relations for the total number of ground states. The latter procedure, which is in principle an approximation, is proposed as an alternative for dealing with complicated systems (for cases where the recursive approach may become impracticable), such as randomly frustrated models; it consists of factorizing the total number of ground states in terms of the number of ground states at each hierarchy level. Some examples of antiferromagnetic Ising models on different fractal lattices are considered, for which both procedures are applied. It is shown that the factorization approach may lead, in some cases, to the exact ground-state entropy, whereas in other cases it yields very accurate (although slightly lower) estimates.
研究了分形晶格上受挫系统的广泛基态熵。提出了两种计算方法，即递归法和因式分解法。在递归法中，计算基于基态总数的精确递归关系。后一种方法原则上是一种近似方法，被提议作为处理复杂系统（如随机受挫模型，在这些情况下递归法可能不可行）的替代方法；它包括根据每个层次水平的基态数对基态总数进行因式分解。考虑了不同分形晶格上反铁磁伊辛模型的一些例子，并对这两种方法都进行了应用。结果表明，因式分解法在某些情况下可能得到精确的基态熵，而在其他情况下则能给出非常准确（尽管略低）的估计。
