potentials.py

#Interaction potentials
"""
This is a library for storing functions that describe each interaction potential
as Haldane pseudo-potentials.
"""

import math
import scipy.special
import mpmath
from usefulTools import norm2 as norm2
import matplotlib
from matplotlib import pyplot as pyplot

V_m = [math.log(i+1) for i in range(10)]
mMax = len(V_m)

def exponentailRepulsion(n, magneticLength):
    alpha = 1
    x = (alpha**2)/(2 + alpha**2)
    return x**(n+1)

def v3(m, magneticLength):
    if m == 3:
        return norm2(m, magneticLength*math.sqrt(2))
    else:
        return 0

def v_k(m, magneticLength):
    if m < mMax:
        return V_m[m]*norm2(m, magneticLength*0.1)
    else:
        return 0
    

def coulomb(m, magneticLength):
    f = scipy.special.gamma
    return 0.5*f(m+0.5)/f(m+1)

def longRange(m, magneticLength):
    alpha = 2
    return ((2*magneticLength)**(-alpha))*mpmath.gammaprod((m+1-(alpha/2),), (m+1,))
"""
y = [1-longRange(i, 1)/norm2(i, math.sqrt(2)) for i in range(30)]
x = [i for i in range(30)]
pyplot.plot(x,y)
pyplot.show()
"""