High-temperature expansion for Ising models on quasiperiodic tilings

Дата и время публикации : 1999-01-01T11:53:57Z

Авторы публикации и институты :
Przemyslaw Repetowicz
Uwe Grimm
Michael Schreiber

Ссылка на журнал-издание: J. Phys. A: Math. Gen. 32 (1999) 4397-4418
Коментарии к cтатье: 24 pages, 8 figures (EPS), uses IOP styles (included)
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech, cond-mat.dis-nn

Краткий обзор статьи: We consider high-temperature expansions for the free energy of zero-field Ising models on planar quasiperiodic graphs. For the Penrose and the octagonal Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a by-product, we obtain exact vertex-averaged numbers of self-avoiding polygons on these quasiperiodic graphs. In addition, we analyze periodic approximants by computing the partition function via the Kac-Ward determinant. For the critical properties, we find complete agreement with the commonly accepted conjecture that the models under consideration belong to the same universality class as those on periodic two-dimensional lattices.

Category: Physics