2D Ising model with competing orders
$$ S=K\sum_{\langle i,j\rangle} s_i s_j + V \sum_{\langle \langle i,j\rangle\rangle} s_i s_j $$ green bonds are nearest couplings \(\langle i,j\rangle\); the red bonds are next nearest couplings \(\langle\langle i,j\rangle\rangle\)
the system gets very rich phase diagram, for example, when

updating speed=100 Coupking \(K\)=0.5 Coupking \(V\)=0.5

physics experiments you can do!

1. explore the phases

when \(K=0\), the system can be divided into two decoupled sub-systems.
\(V=-\infty\) gives two anti-ferromagnetic system, according to their relative postition, we can have either vertial strip order or horizantal strip order.

2. hysteresis effect

  1. tune \(V\) to the largest postive value
  2. tune \(K\) to zero.
  3. set updating speed to maximum
  4. wait some time, until domain wall disappear
  5. now tune \(K\) slowly from 0 to 0.2
  6. and then tune \(K\) slowly from 0.2 to -0.2
  7. go back tune \(K\) slowly from -0.2 to 0.2
  8. you will see a hysteresis effect happen near \(K=\pm 0.14\), for \(V=1\)

3. neutron scattering

I will add FFT feature later, where you can see the scattering plot.