Ferromagnetic phase transitions of inhomogeneous systems modelled by square Ising models with diamond-type bond-decorations

摘要

The two-dimensional Ising model defined on square lattices with diamond-type bond-decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems. The model is studied analytically under the bond-renormalization scheme. For an n-level decorated lattice, the long-range ordering occurs at the critical temperature given by the fitting function (k(B)T(c)/J)(n) = 1.6410 + (0.6281)exp[ - (0.5857)(n)], and the local ordering inside n-level decorated bonds occurs at the temperature given by the fitting function (k(B)T(c)/J)(n) = 1.6410 - (0.8063) exp[ - (0.7144)(n)]. The critical amplitude A(sin g)((n)) of the logarithmic singularity in specific heat characterizes the width of the critical region, and it varies with the decoration-level n as A(sin g)((n)) = (0.2473) exp[ - (0.3018)(n)], obtained by fitting the numerical results. The cross over from a finite-decorated system to an infinite-decorated system is not a smooth continuation. For the case of infinite decorations, the critical specific heat becomes a cusp with the height c((n)) = 0.639852. The results are compared with those obtained in the cell-decorated Ising model. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 23]