Computational Physics - Department of Physics

13.6 Selected Results for the Ising Model 443

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" 10 × 10 "

kBT

E/

J

1.6 1.8 2 2.2 2.4 2.6

0

-0.5

-1

-1.5

-2

-2.5

Fig. 13.5Average energy per spin as function of the lattice size for the two-dimensional Ising model.

We note that with increasing lattice size we approach a steeper line and the transition from
a smaller magnetisation to a larger one becomes sharper. This is a possible sign of a phase
transition, where we move from a state where all spins (or most of them) align in a specific
direction (high degree of order) to a phase where both spin directions are equally probable
(high degree of disorder) and result in zero net magnetisation. The ordered phase at low
temperatures is called a ferromagnetic phase while the disordered phase is called the param-
agnetic phase, with zero net magnetisation. Since we are plotting the absolute value, our net
magnetisation will always be above zero since we are taking the average of a number which
is never negative.

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" 10 × 10 "

kBT

〈|M

|〉

1.6 1.8 2 2.2 2.4 2.6 2.8 3

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Fig. 13.6Absolute value of the average magnetization per spin as function of the lattice size for the two-
dimensional Ising model.