Results

    Following results were simulated on phelafel. Animated visualization of the spins were generated using Aviz software.

Visualization


Figure 1: L = 5 , 0.01 < Temperature < 1 , h = 1 , runs = burn_runs = 100000 . For better 3D visual perception click here.
In the figure presented 3D spin lattice, red cones represent $\sigma=+1$ and black cones represent $\sigma=-1$. We can notice a frustration of some spins, those who flip back and forth. Spins are not aligned with magnetic field due to random interactions.

Magnetization


Figure 2: 0.01 < Temperature < 6 , h = 0 , runs = burn_runs = 100000 .
Magnetization for lattices of different size. Greater magnetization seen for smaller lattice. Below $T\approx2 [J] $ the system seems to be unstable and noisy. Magnetization observed is independent of temperatures above $T\approx3 [J] $ for all lattice sizes.

Energy


Figure 3: 0.01 < Temperature < 6 , h = 0 , runs = burn_runs = 100000 .
Energy per spin observed nearly constant below $T\approx2 [J] $. This is also the minimal energy observed in simulation, since the temperatures are small. Upon heating, the energy increases. Energy seems independent of system size, except maybe at very low temperatures.

Figure 4: 0.01 < Temperature < 1.5 , h = 0 , runs = burn_runs = 100000 .
Zoom on previous plot. We notice small decrease in energy for system with L = 10 . Such behaviour may imply a meta-stable phase of the system. This statement requires a deeper investigation.

Heat capacity


Figure 5: 0.01 < Temperature < 6 , h = 0 , runs = burn_runs = 100000 .
Heat capacity has a general form of $\lambda$ phase transition line found in many importrant condensed matter systems. From this we can deduce that system undergoes a phase transition, nearly at $T_{c}\approx2 [J]$. Heat capacity is independent of system size.