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# Author: 8230W #

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# Code Description #

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# Code to produce 3D lattice plots to help for visualisation of spin behaviour in real space #

# produces plots of spins for flippability, number of neighbours as well as sub plots of a cubic system #

# for ease of visualisation #

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# Inputs #

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# Reads in CSV files containing Lattice Spin data, Lattice Spin Flip Data, Lattice Neighbour data #

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# Outputs #

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# produces 4 plots, 2 of flippability denoted by lattice size and spin direction on a full lattice and #

# cubic lattice plot and 2 of lattice neighbours and flippability #

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import matplotlib.pyplot as plt

import matplotlib

import pandas as pd

from mpl_toolkits.mplot3d import Axes3D

import numpy as np

import math as mth

from itertools import product, combinations

from matplotlib import rc

# activate latex text rendering

rc('text', usetex=True)

#set rc parameters for plotting

matplotlib.rcParams.update({'font.size': 60})

matplotlib.rcParams['axes.labelpad'] = 70

plt.rcParams["font.family"] = "Times New Roman"

plt.set_cmap("jet")

#import data to be plotted

data = pd.read_csv(r'C:\Users\Theo\PartIII\FINAL_LatticeSpinsT05.csv')

Lattice = pd.DataFrame(data, columns = ['i', 'j', 'k', 'Spin'])

data = pd.read_csv(r'C:\Users\Theo\PartIII\FINAL_LatticeT05.csv')

LatticeSize = pd.DataFrame(data, columns = ['i', 'j', 'k', 'Spin Flips'])

data = pd.read_csv(r'C:\Users\Theo\PartIII\FINAL_NearestNeighbourT05.csv')

LatticeNeighbours = pd.DataFrame(data, columns = ['i', 'j', 'k', 'Neighbours'])

#assign gif and ax for full lattice plot

fig = plt.figure()

ax = plt.axes(projection="3d")

#convert lattice indexing to cartesian coordinates

x_coord = (Lattice['i']+Lattice['j'])

y_coord = (Lattice['k']+Lattice['i'])

z_coord = (Lattice['k']+Lattice['j'])

#assing data sets to determine colour,size etc.

Neighbours = LatticeNeighbours['Neighbours']

Spin_Size = 10000*(LatticeSize['Spin Flips']+0.05)

Spin = np.abs(Lattice['Spin']) #use this for spin colour if just trying to differentiate between spins and non spins

#list to contain nearest neighbour number data to create a colour map from

Spin_Colour = []

#go through data set and assign either 0 or 1 for spins with either even or odd neighbours for the colourmap, assign the value 3 for non-spins

for i in range(len(Neighbours)):

if Spin[i] != 0:

Spin_Colour.append(Neighbours[i]%2)

else:

Spin_Colour.append(3)

#plot data

ax.scatter3D(x_coord,y_coord,z_coord, s = Spin_Size, c = Spin_Colour)

#add text labels of number of neighbours

#for i in range(len(Neighbours)):

# ax.text(x_coord[i],y_coord[i],z_coord[i], '%d' % (int(Neighbours[i])), size=20, zorder=1,

# color='k')

# draw cube

r = [0,2,4,6,8]

for s, e in combinations(np.array(list(product(r, r, r))), 2):

if np.sum(np.abs(s-e)) == r[1]-r[0]:

ax.plot3D(*zip(s, e), color="b", linewidth = 0.5)

#square up axes

ax.set_aspect("equal")

plt.show()

#Assing axes for the 2x2 cubic unit cell plot

ax2 = plt.axes(projection="3d")

#lists to contain subset of coordinates and colour/size data for the 2x2 cell

x_coord_sub = []

y_coord_sub = []

z_coord_sub = []

Spin_Size_sub = []

Spin_Colour_sub = []

#append valid data values for that list

for i in range(4,9,1):

for j in range(4,9,1):

for k in range(4,9,1):

for n in range(len(x_coord)):

if x_coord[n] == i and y_coord[n] == j and z_coord[n] == k:

x_coord_sub.append((x_coord[n]-4)/2)

y_coord_sub.append((y_coord[n]-4)/2)

z_coord_sub.append((z_coord[n]-4)/2)

Spin_Size_sub.append(Spin_Size[n])

Spin_Colour_sub.append(Spin_Colour[n])

#plot data

ax2.scatter3D(x_coord_sub,y_coord_sub,z_coord_sub, s = 1000*Spin_Size_sub, c = Spin_Colour_sub)

ax2.set_xlabel('x (l.u.)')

ax2.set_ylabel('y (l.u.)')

ax2.set_zlabel('z (l.u.)')

ax2.set_aspect("equal")

#plot background cubes for aif of visualisation

r = [0,1,2]

for s, e in combinations(np.array(list(product(r, r, r))), 2):

if np.sum(np.abs(s-e)) == r[1]-r[0]:

ax2.plot3D(*zip(s, e), color="b", linewidth = 0.5)

plt.show()

#assing fig and axes for sublattice plot of full lattice data

fig1 = plt.figure()

ax1 = plt.axes(projection="3d")

#import data for sublattice to be used to pick required spins

data = pd.read_csv(r'C:\Users\Theo\PartIII\AFMSublattice.csv')

SubLattice = pd.DataFrame(data, columns = ['i', 'j', 'k', 'Spin'])

#booleans to be used to select data

Spin_Coords = Lattice['Spin'] != 0

Fixed = LatticeSize['Spin Flips'] < 0.1

#use booleans to choose subsets of original data sets required for the sublattice plots

LatticeNeighbours = LatticeNeighbours[Spin_Coords & Fixed]

LatticeSize = LatticeSize[Spin_Coords & Fixed]

SubLattice = SubLattice[Spin_Coords & Fixed]

Spin_Coords = Lattice[Spin_Coords & Fixed]

#convert from FCC indexing to cartesian coords

x_coord = (Spin_Coords['i']+Spin_Coords['j'])/2

y_coord = (Spin_Coords['k']+Spin_Coords['i'])/2

z_coord = (Spin_Coords['k']+Spin_Coords['j'])/2

#colour & size arrays

Neighbours = LatticeNeighbours['Neighbours']

Spin_Size = 10000*(LatticeSize['Spin Flips']+0.05)*SubLattice['Spin']

Spin = Spin_Coords['Spin'] #use this for spin colour if just trying to differentiate between spins and non spins

#plot data

ax1.scatter3D(x_coord,y_coord,z_coord, s = Spin_Size, c = Spin)

#text labels for number of nearest neighbours

#for i in range(len(Neighbours)):

# ax.text(x_coord[i],y_coord[i],z_coord[i], '%d' % (int(Neighbours[i])), size=20, zorder=1,

# color='k')

#square plot

ax1.set_aspect("equal")

ax1.set_xlabel('x (l.u.)')

ax1.set_ylabel('y (l.u.)')

ax1.set_zlabel('z (l.u.)')

plt.show()

#assign axes for 2x2 cubic cell plot of sublattice

ax2 = plt.axes(projection="3d")

#lists to contain subset of coordinates and colour/size data for the 2x2 cell

x_coord_sub = []

y_coord_sub = []

z_coord_sub = []

Spin_sub = []

Spin_Colour_sub = []

#assign valid data

for i in range(4,11,2):

for j in range(4,11,2):

for k in range(4,11,2):

for n in range(len(x_coord)):

if x_coord.iloc[n] == i and y_coord.iloc[n] == j and z_coord.iloc[n] == k:

x_coord_sub.append((x_coord.iloc[n]-4)/2)

y_coord_sub.append((y_coord.iloc[n]-4)/2)

z_coord_sub.append((z_coord.iloc[n]-4)/2)

Spin_Size_sub.append(Spin_Size.iloc[n])

Spin_sub.append(Spin.iloc[n])

#plot data

ax2.scatter3D(x_coord_sub,y_coord_sub,z_coord_sub, s = 1000*Spin_Size_sub, c = Spin_sub)

#square data

ax2.set_aspect("equal")

ax2.set_xlabel('x (l.u.)')

ax2.set_ylabel('y (l.u.)')

ax2.set_zlabel('z (l.u.)')

#create background cube

r = [0,1,2,3]

for s, e in combinations(np.array(list(product(r, r, r))), 2):

if np.sum(np.abs(s-e)) == r[1]-r[0]:

ax2.plot3D(*zip(s, e), color="b", linewidth = 0.5)

plt.show()