<jupyter_start><jupyter_text>2. Lattice Energy/Magnetization Evolution<jupyter_code>myplot(EnergyTime)
myplot(MagTime)
myplot(EnergyTime3)
myplot(MagTime3)<jupyter_output><empty_output><jupyter_text>In your script, compute the energy and magnetization per spin for 1000 time steps (cycling through the lattice to find a new microstate) for T = 1.1 and plot them vs. the Monte Carlo time steps. Do these plots make sense?The plots seem to make sense. At low temperature there are few fluctuations and the lattice remains near the lowest energy. As the temperature is increased the fluctuations increase.  3. Energy vs. Lattice Size<jupyter_code>myplot(EnergyvsSize2)
myplot(EnergyvsSize)<jupyter_output><empty_output><jupyter_text>Generate a plot showing how the lattice size affects the calculated energy and explain what is happening.We should expect the lattice energy to increase as the lattice size increases. A small lattice is essentially a single domain and due to the periodic boundary conditions a dipole  may interact with the same neighbor twice. As the lattice size increases, the percentage of dipoles that are on the edge decreases and our system properties will be dominated by the bulk and we have a decent estimate of a true thermodynamic system.At T = 1.1 [$\epsilon$/K] lattices of all sizes in this range give similar energies. This must be a very cold temperature for the lattice when compared to T = 1.8[$\epsilon$/K]  4. Energy/Magnetization vs Temperature<jupyter_code>myplot(EnergyTemp)
myplot(MagTemp)<jupyter_output><empty_output><jupyter_text>There is a phase transition occurring when the temperature changes: explain what is happening to the spin lattice as a function of temperature. I suggest you plot the absolute value of average M: why would you want to do this?The Lattice magnetization becomes nonzero when passing beneath the critical temperature $T_c$ = 2.2 [e/K]. We may want to plot using the absolute value of the average magnetization because it is possible for the simulation to reverse all of the spins on the lattice without having a large affect on the average energy. Physically, this means that $T_c$ the dipoles will spontaneously align either pointed up or down.  5. Specific Heat<jupyter_code>myplot(SpecHeat)<jupyter_output><empty_output><jupyter_text>What temperature does the transition occur at and what is happening here?Near T = 2.2 we see the specific heat begin to spike which indicates a phase transition. The specific heat rises sharply due to the large amount of energy necessary to flip the dipole system from arranged state to the randomly oriented state.  6. Magnetic Field and Hysteresis<jupyter_code>myplot(Hysteresis)
myplot(Hysteresis2)
myplot(Hysteresis3)<jupyter_output><empty_output>
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