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

Abstract

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 BT 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 BT m/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.