Fig. 1

(Color online) Schematic representations of the spin-1/2 XYZ chain with finite length of (a) 6 particle, and (b) 10 particle, under periodic boundary conditions. $J$ denotes XYZ Heisenberg exchange interaction between each adjacent spins."

Fig. 2

(Color online) Low-temperature $(T=0.1J_z)$ magnetization and magnetic susceptibility as functions of the longitudinal magnetic field $B_z/J_z$ for several fixed values of the transverse field $B_x/J_z$ , and an arbitrary angle $\theta={\pi}/{30}$ under the condition $b_z=b_x=\lambda=0$. The system is considered in the presence of external homogeneous magnetic fields for which coupling constants have been conventionally taken as $J_{x}=8J_z$ and $J_y=10J_z$. Panels (a) and (c) correspond to the spin-1/2 XYZ model of finite length $N=6$; panels (b) and (d) correspond to the chain of length $N=10$. Insets show the corresponding magnetization and magnetic susceptibility curves for different angle $\theta={\pi}/{10}$."

Fig. 3

(Color online) Magnetization and magnetic susceptibility as functions of the longitudinal magnetic field $B_z/J_z$ for several fixed values of the transverse field $B_x/J_z$ at low temperature $(T=0.1J_z)$ and finite angle $\theta={\pi}/{30}$. Inhomogeneous property is considered for all applied magnetic fields such that; $b_z=0.6J_z$, $b_x=0.3J_z$, and $\lambda=J_z$. Coupling constants have been set as Fig. 2. Figures 3(a) and 3(c) are associated to the chain with finite length $N=6$; panels (b) and (d) correspond to that of the length $N=10$. Insets show the corresponding magnetization and magnetic susceptibility curves for higher transverse staggered field $B_x/J_z$ by setting $\theta={\pi}/{10}$."

Fig. 4

Temperature dependences of the specific heat of the 1-D XXZ spin chain under various fixed values of the longitudinal magnetic field $B_z/J_z$. Other external magnetic fields and parameters are taken as $B_x=J_z$, $\theta={\pi}/{30}$, $J_{x}=8J_z$ and $J_y=10J_z$. All applied magnetic fields are also considered as homogeneous fields such that: $b_z=0$, $b_x=0$, and $\lambda=0$. (a) The specific heat of the chain with finite length $N=6$, and (b) $N=10$. Insets show the specific heat of the model in the presence of higher transverse staggered field as $\theta={\pi}/{10}$."

Fig. 5

(Color online) Temperature dependences of the specific heat of the 1-D XYZ spin chain under various fixed values of the longitudinal magnetic field $B_z/J_z$. Other external magnetic fields and parameters are as in Fig. 4. Here, all applied magnetic fields have been considered as inhomogeneous fields such that: $b_z=0.6J_z$, $b_x=0.3J_z$, and $\lambda=J_z$. (a) The specific heat as a function of the temperature for the chain with finite length $N=6$, and (b) $N=10$. Insets show the specific heat of the model versus temperature in the presence of higher transverse staggered field as $\theta={\pi}/{10}$."