Pearson’s Results

In 1991 Pearson, calculated the exact partition function for the 4x4x4 Ising model. Plotting Pearson’s results against my own. I also managed to calculate this using my program, the results are compared

Pearson vs. Yogi

This page displays my results against R.B Pearsons.

Zero Distribution of 5x5x10

Animation of 5x5xN (where 2 <= N <= 10)

Zero distribution for Q=2 5x5xN

A study of the boundary conditions. The left column of results are my original ones. The right column is trivial palindromes of the polynomials found.

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Zeros of 3 State 4x4x10 Potts Model

Fig 1: Periodic boundary conditions in the two short direction

3 state animation of 4x4xN (where 2 <= N <= 10)

Zero distribution for Q=3 4x4xN

A study of the boundary conditions. The left column of results are my original ones. The right column is trivial palindromes of the polynomials found.

Animation of the 3 state 4x4xN

Zero Distribution of 4 state Potts Models

Below are zero distributions for the 3 x 4 x 10 Potts lattice model with Q = 4. This is for the purpose of taking a closer look at boundary conditions. The dimesions are height x width x depth

Fig 1: No Boundary conditions	Fig 2: Periodic Boundary conditions in dimesions along the width and height
Fig 3: Periodic Boundary conditions in dimensions along the width only.	Fig 4: Periodic Boundary conditions in dimensions along the height only.

Zero Distribution of 5 state Potts Models

Below are zero distributions for the 3 x 3 x 10 Potts lattice model with Q = 5. This is for the purpose of taking a closer look at boundary conditions. The dimesions are height x width x depth

Fig 1: No Boundary conditions	Fig 2: Periodic Boundary conditions in dimesions along the width and height
Fig 3: Periodic Boundary conditions in dimensions along the width only.	Fig 4: Periodic Boundary conditions in dimensions along the height only.

The zero’s of my largest 3 dimensional results.

2-state 4x6x10 lattice

2-state 5x5x10 lattice (anti-ferromagnetic on right)

 
 

2-state 4x4x10 lattice, with period boundary conditions

A closer look at the zero’s pinching the real axis

On this page we take a closer look at the “pinch” of the two outer arms of zeros on the real axis. A plot of the anti-ferromagnetic zeros of a 5x5x10 lattice with q=2 is shown below. The parametric graph f(x(t), y(t)) = acos(t)(1+cos(t+k)) + b, csin(t)(1+cos(t+k))+d is also plotted. Where a, b, c, d and k are real value constants.

The figure below is a closer look at the top right arm.

Specific Heat

Q = 2

Animation of Potts model with Q = 2

Below are animations of all the 2 state zero distributions found.

Animation 1: No boundary conditions	Animation 2: Boundary condition in both directions
Animation 3: Boundary Conditions only connecting the rows	Animation 4: Boundary Conditions only connecting the columns

Animation of Potts model with Q = 3

Animation of Potts model with Q = 4

Animation of Potts model with Q = 5

Animation of Potts model with Q = 6

2D Results

• 6 state: 8x8, 7x7 (periodic boundary conditions)
• 3 state:12x16</li> </ul> </div> </div>