You're seeing a different graph since you're finding the root around the initial value [-1, 1] in MATLAB while the root is around the initial value 1 in Mathematica. If you change your call to "fzero" from:
x = fzero(fun, [-1, 1]);
To:
x = fzero(fun, 1);
The graph is as expected. Here's the complete code for your reference:
clearvars; clc; close all; fclose all; format compact; format short;
B = @(J, x) ((2*J+1)/(2*J))*coth(((2*J+1)/(2*J))*x)-(1/(2*J)).*coth((1/(2*J))*x);
J = 1/2;
n = 101;
tau_array = linspace(0, 1.2, n);
m_array = zeros(1, n);
for i = 1:n
tau = tau_array(i);
fun = @(m) (B(J, ((3*J)/(J+1))*m*(1/tau)) - m);
x = fzero(fun, 1); % Note the change from [-1, 1] to 1
m_array(i) = x;
end
fig = figure();
ax = axes(fig);
plot(ax, tau_array, m_array,"LineWidth",2,"Color","red");
xlabel('Reudced temperature, \tau');
ylabel('Redueced magnetization, m')
title('m as a function of \tau')
ax.TickDir = 'out';
Please note that only the y-axis limits are different from the expected graph. You can change it easily using the "ylim" function.
Please refer to the following links for more information:
- "fzero" documentation - https://www.mathworks.com/help/releases/R2023a/matlab/ref/fzero.html.
- "ylim" documentation - https://www.mathworks.com/help/releases/R2023a/matlab/ref/ylim.html.
Hope this helps!
