Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 2 Blume-Capel Model Li,Zimeng PB06203182
Mean-Field Blume Capel Model
Edited by Li, Zimeng
Contents:
1. Definition
1.1 Tricritical Ising Model
1.2 Blume, Emery and Griffiths (BEG) Model
2. Phase Transition Diagram
3. Mean Field Solution of the Blume-Capel model
3.1 One Dimension Case
3.2 Two Dimension Case
3.3 Observable and Critical Exponents
1. Definition
In order to introduce in the Blume Capel Model, we would like to take a review of the
tricritical Ising model and the Blume, Emery and Griffiths (BEG) Model.
1.1 Tricritical Ising Model
The first generalization of Ising criticality is obtained when considering an Ising
antiferromagnet with Hamiltonian
, where is called the staggered magnetic
field.
It is easily drawn that the tricritical Ising model falls to normal Ising Model when
=0. When considering the Hamiltonian above fully, we can draw the phase
diagram of the tricritical Ising model.See Fig 1.1.1