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

• Published in: Physica A Vol. 321; no. 3; pp. 498 - 518
• Main Authors: Huang, Ming-Chang, Luo, Yu-Pin, Liaw, Tsong-Ming
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.04.2003
• Subjects: Critical point; Fractal lattice; Ising model; Phase transition; Ising model; Critical point; Fractal lattice; Phase transition
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(02)01555-8

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.