Dimer coverings on the sierpinski gasket

Shu Chiuan Chang, Lung Chi Chen

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23 引文 斯高帕斯(Scopus)


We present the number of dimer coverings N d (n) on the Sierpinski gasket SG d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as S_SG_=n N_d(n)v(n) , is calculated to be ln∈(2)/3 exactly for SG 2. The numbers of dimers on the generalized Sierpinski gasket SG d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln∈(6)/7, ln∈(28)/12, ln∈(200)/18, respectively. The number of dimer coverings for SG 3 is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of S_SG_{d}} with d=3,4,5 can be evaluated with more than a hundred significant figures accurate.

頁(從 - 到)631-650
期刊Journal of Statistical Physics
出版狀態Published - 2008 5月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學


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