Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 2 Blume-Capel Model Li,Zimeng PB06203182
Fig 1.1.1
In the above diagram, the (broken) first-order line and the (full) line of Ising critical
points (second-order) meet at the tricritical point (Bt,Tt)shown as black dot.
Phase diagram of above has been realized in 3D metamagnetic systems such as Ising
model with annealed vacancies,modeled by a vacancy variable
and the Hamiltonian
If we define , which takes the value , then we obtain the Blume Capel
model with Hamiltonian
(1.1.1)
1.2 Blume, Emery and Griffiths (BEG) Model
Historically, the Blume-Capel model is a simplification of the BEG model.The spin-1
model
was introduced by Blume, Emery and Griffiths. Here
J is the usual Ising coupling, a is the constant of biquadratic exchange and the parameter