willpugs / stat-mech-monte-carlo Goto Github PK

Implement the Metropolis rule and include the option to use this rule in the simulations.

The full_sim_1d function when asked to simulate for energies returns a ufunctypeerror for addition in the energy_change_1d function.

I think this is because at some point the names of two variables get mixed up but I cannot find which variables or where this happens (I think it is most likely the grid/strip or idx variable that gets mixed up somehow).

Need to define a function to find the average energy of a system at various temperatures then use this relation to find Cv vs T.

To-do in 1D and 2D.

We have two possible values for the H=0 critical exponents of the 2D Ising model.

Exact results from Onsager:

• $\alpha=0(log)$
• $\beta=1/8$
• $\gamma=7/4$
• $\delta=15$
• $\eta=1/4$
• $\nu=1$

Mean field results (applies to our simulation):

• $\alpha=0(disc.)$
• $\beta=1/2$
• $\gamma=1$
• $\delta=3$
• $\eta=0$
• $\nu=1/2$

Do we take the absolute value of when running full_sim functions?

The functions for the expectation values of in 1D and 2D assume that >= 0 always.

Correlations between spins in the 1D H=/=0 case are not what we would expect, there is too little correlation.

More in-text citations are need throughout the written report in the .ipynb files.

Having problems fitting the <m> function to the data points.

• <m> uses conditional statements to return the proper value, the curve_fit function does not work with this sort of function.
• There is a runtime error when raising certain values to a fractional power. Numpy does not allow raising negative numbers to a fractional power but all the numbers in our array should be positive.
• There is a runtime/zero-division error when we give sigma values as input to curve_fit.

Should the correlation function <Si*Si+r> be strictly positive? If so where do we take the absolute value; before or after taking the average?

Sequential iteration through an Ising model grid may not satisfy detailed balance. A better implementation would be to test the flip at each spin site in a random order.