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

TL;DR

This paper analytically investigates ferromagnetic phase transitions in inhomogeneous two-dimensional Ising models with diamond-type bond decorations, revealing how critical temperatures and specific heat singularities depend on decoration levels.

Contribution

It provides explicit analytical expressions for critical temperatures, specific heat behavior, and crossover phenomena in decorated Ising models, extending understanding of inhomogeneous ferromagnetic systems.

Findings

Critical temperature decreases with decoration level n.

Critical specific heat approaches a cusp value as n increases.

The transition from finite to infinite decoration is non-smooth.

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 as $(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 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 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.