Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 2 Blume-Capel Model Li,Zimeng PB06203182
vanished at
or
[2] Blume-Capel Model
The Blume-Capel model is different from [1] in its additional term
, which allows
the coefficient of in the free energy to change sign.Therefore the coefficient of
may happen to be negative, and so the above diversity of free energy with respect to M
can be interpreted in the following figure:
Here , similar to
Fig 3.4
in [1], is also the first order phase transition critical point. (When
in the free energy vanishes)
From Sec. 2 we know there is a tricritical point where the first order phase transition
turns into the second order phase transition. The tricritical point can be obtained when
both and vanishes.
3.2 Two Dimension Case
We give the result here without proof. On a square lattice, the Blume-Capel model
exhibits two equivalent, ferromagnetic ground states A and B, for ; and
one ground state, , for . At (D/J) (with (2) = 0) the ferromagnetic phases A
and B undergo an order-disorder transition which is second-order for < 1.945,
tricritical for D/J 1.945 and first order for 1.945 < (d=2).