The two-dimensional Ising model defined on square lattices with diamond-typebond-decorations is employed to study the nature of the ferromagnetic phasetransitions of inhomogeneous systems. The model is studied analytically underthe bond-renormalization scheme. For an $n$-level decorated lattice, thelong-range ordering occurs at the critical temperature given by the fittingfunction as $(k_{B}T_{c}/J)_{n}=1.6410+(0.6281) \exp [ -(0.5857) n] $, and thelocal ordering inside $n$-level decorated bonds occurs at the temperature givenby the fitting function as $(k_{B}T_{m}/J)_{n}=1.6410-(0.8063) \exp [ -(0.7144)n] $. The critical amplitude $A_{\sin g}^{(n)}$ of the logrithmic singularityin specific heat characterizes the width of the critical region, and it varieswith 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 afinite-decorated system to an infinite-decorated system is not a smoothcontinuation. For the case of infinite decorations, the critical specific heatbecomes a cusp with the height $c^{(n)}=0.639852$. The results are comparedwith those obtained in the cell-decorated Ising model.
展开▼
机译:利用具有菱形粘结修饰的方形晶格上定义的二维伊辛模型,研究非均匀系统的铁磁相变性质。该模型在键重整化方案下进行了分析研究。对于$ n $级别的装饰晶格,在由拟合函数给出的临界温度下,远程排序发生为$(k_ {B} T_ {c} / J)_ {n} = 1.6410 +(0.6281)\ exp [ -(0.5857)n] $,并且$ n $级修饰键内的局部排序发生在拟合函数给定的温度下,即$(k_ {B} T_ {m} / J)_ {n} = 1.6410-(0.8063) )\ exp [-(0.7144)n] $。对数奇异性在比热中的临界振幅$ A _ {\ sin g} ^ {(n)} $表征了临界区域的宽度,并且随装饰水平$ n $的变化而变化为$ A _ {\ sin g} ^ { (n)} =(0.2473)\ exp [-(0.3018)n] $,通过拟合数值结果获得。从无限装饰系统到无限装饰系统的过渡不是平稳的延续。对于无限装饰的情况,临界比热成为高度$ c ^ {((n)} = 0.639852 $)的尖峰。将结果与在单元格装饰的伊辛模型中获得的结果进行比较。
展开▼