6.4b Magnetization labs

Source: Lab ideas from Computational Physics (Landau, Páez, Bordeianu), §6.4. Rewritten as original drills. Continues 6.4 Magnetization search.

At fixed reduced temperature $t$, root-find $f(m,t)=m-\tanh(m/t)=0$ for the nontrivial branch ($m>0$ when t<1). Use math.tanh. Bisection and Newton conventions match §6.2b–6.3b ($\varepsilon=10^{-14}$; Newton uses forward difference $\delta x=10^{-6}$).

Formula refresh

Warm up: pick the matching equation among lookalikes (same walk as the theory lesson).

Labs

Activity: Sign change at $t=0.5$

Evaluate $f(m,0.5)$ at $m=0.5$ and $m=1.0$. Print both with 10 decimals, space-separated.

No input.

Write-ups

0/3 solved

6.4b.W1

Using “both”, “transcendental”, and “tanh”, explain:

Why can you not solve $m=\tanh(m/t)$ for $m(t)$ by algebra alone?

Minimum 3 words. Your answer must include: “both”, “transcendental”, “tanh”.

0 words/ 3 min

Meet the writing requirements, then you can open the model answer.

Explorers

Next: 6.5 Lagrange interpolation — from searching self-consistent $m(t)$ to interpolating tabulated data.