- #1

JD_PM

- 1,131

- 158

## Homework Statement

The mean field solution for the Ising model is:

$$m = tanh[\beta (mJz + H)]$$

**I wanted to carry out a dimensional analysis in order to verify the equation.**

## Homework Equations

$$m = tanh[\beta (mJz + H)]$$

## The Attempt at a Solution

Knowing that:

$$[m] = \frac{A}{L}$$

$$[\beta] = \frac{T^2}{ML^2}$$

$$[J] = \frac{ML^2}{T^2}$$

$$[H] = \frac{A}{L}$$

As dimensions of ##\beta## and ##J## cancel out and ##z## is dimensionless you get the desired dimensions, so no problem with the ##\beta mJz## component.

However ##\beta H## does not yield the desired dimensions,

**so I guess I made a mistake coping on my lecture notes and the equation should be:**

$$m = tanh[\beta (mJz) + H)]$$

**Do you agree?**