数据的指数拟合有利于较小的价值？

Question

我正在尝试对数据进行指数拟合以确定该值下降1 / e的点。绘制时，拟合似乎倾向于较小的值，并且没有描绘真实的关系。

import numpy as np 
import matplotlib
matplotlib.use("TkAgg")  # need to set the TkAgg backend explicitly otherwise it introduced a low-level error
from matplotlib import pyplot as plt
import scipy as sc


def autoCorrelation(sample, longTime, temp, plotTau = False ):
# compute empirical autocovariance with lag tau averaged over time longTime

    sample.takeTimeStep(timesteps=1500)  # 1500 timesteps to let sample reach equilibrium
    M = np.zeros(longTime)
    for tau in range(longTime):
        M[tau] = sample.calcMagnetisation()
        sample.takeTimeStep()

    M_ave = np.average(M) #time - average
    M = (M - M_ave)

    autocorrelation = np.correlate(M, M, mode='full')
    autocorrelation /= autocorrelation.max() # normalise such that max autocorrelation is 1
    autocorrelationArray = autocorrelation[int(len(autocorrelation)/2):]
    x = np.arange(0, len(autocorrelationArray), 1)

    # apply exponential fit
    def exponenial(x, a, b):
        return a * np.exp(-b * x)
    popt, pcov = curve_fit(exponenial, x, np.absolute(autocorrelationArray)) # array, 2d array
    yy = exponenial(x, *popt)
    plt.plot(x, np.absolute(autocorrelationArray), 'o', x, yy)
    plt.title('Exponential Fit of Magnetisation Autocorrelation against Time for Temperature = ' + str(T) + ' J/k')
    plt.xlabel('Time / Number of Iterations ')
    plt.ylabel('Magnetisation Autocorrelation')
    plt.show()

    # prints tau_e value b from exponential a * np.exp(-b * x)
    print('tau_e is ' + str(1/popt[1])) # units converted to time steps by taking reciprocal






if __name__ == '__main__':

#plot autocorrelation against time
    longTime = 100
    temp = [1, 2, 2.3, 2.6, 3, 4]
    for T in temp:
        magnet = Ising(30, T)  # (N, temp)
        autoCorrelation(magnet, longTime, temp)

注意：Ising是另一个.py文件中的类，其中包含功能takeTimeStep和calcMagnetisation。

期望更大的tau_e值