A simple and famous model of certain magnetic materials is the Ising model in(adsbygoogle = window.adsbygoogle || []).push({});

which each of N atoms is modeled as a simple spin which can point upwards or

downwards. The magnetization of the material is proportional to the number of up

spins minus the number of down spins (each spin has a certain magnetization associated

with it).

Let's consider N spins in a row (as shown below). Let the "magnetization" be M,

where M is the number of up spins minus the number of down spins. Each spin is

constantly changing its direction from up to down and vice versa according to some

complex dynamics. Assume the dynamics of one spin are independent of other spins.

↑↓↓↓↑↑↓↑↓↓↑↓↓↑↓↑↑↓↓↓↑↓

(i) Clearly state a postulate on the spin configurations which will help us calculate

probabilities of different spin configurations.

(ii) Using (i), calculate the probability of a certain M value P(M) exactly.

(iii) Show P(M) is a Gaussian in the large N limit and sketch it.

(iv) Estimate the probability that M is larger than 0.1% of N when N takes the value of

Avogadro’s constant, 6x1023

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help with solution

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**