Skills

Physics 11: Statistical Mechanics

14 weeks · 3 milestones

Ensembles, partition functions, quantum gases and phase transitions. Course 11 of the Varsity Curriculum: Physics. Free sources only.

Part of: Physics · Proves for: UG

Milestone map

3 milestones

Ensembles and the partition function

5 weeks (about 12 hrs/week)

Work through the 8.333 notes on probability, kinetic theory and classical statistical mechanics. Then solve the 8.333 problem sets for these topics, then review sets 1–2. Self-check: MIT 8.333 exam review problems with solutions.

Proof required

Link the public repo with the 8.333 problem sets for these topics, then review sets 1–2 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Each ensemble is chosen for a stated reason.
Thermodynamic quantities come from the partition function.
Review sets are marked against their solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.333 problem sets for these topics, then review sets 1–2, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics, unit 1: Ensembles and the partition function
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Each ensemble is chosen for a stated reason.
Thermodynamic quantities come from the partition function.
Review sets are marked against their solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Quantum gases and phase transitions

5 weeks (about 12 hrs/week)

Work through the 8.333 notes on quantum statistics and interacting systems. Then solve the 8.333 problem sets for these topics, then review set 3. Self-check: MIT 8.333 exam review problems with solutions.

Proof required

Link the public repo with the 8.333 problem sets for these topics, then review set 3 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Bose and Fermi statistics are used where each applies.
Low-temperature limits are checked.
The review set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.333 problem sets for these topics, then review set 3, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics, unit 2: Quantum gases and phase transitions
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Bose and Fermi statistics are used where each applies.
Low-temperature limits are checked.
The review set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Find the Ising transition by Monte Carlo

5 weeks (about 12 hrs/week)

Make a notebook that runs a Metropolis Monte Carlo simulation of the two-dimensional Ising model and estimates its critical temperature. Measure the absolute magnetisation, susceptibility and heat capacity across temperatures for three lattice sizes, and compare with the exact value k_B·T_c = 2.269 J.

Proof required

Link the public repo with the notebook, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

The runs are long enough to settle, and that is shown.
T_c is extrapolated from the peak positions using T_c(L) − T_c ∝ 1/L, with an uncertainty from the fit.
Errors from correlated samples are handled.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A notebook that runs a Metropolis Monte Carlo simulation of the two-dimensional Ising model and estimates its critical temperature, in a public repo.

Steps

Write down what you expect before you start.
Measure the absolute magnetisation, susceptibility and heat capacity across temperatures for three lattice sizes, and compare with the exact value k_B·T_c = 2.269 J.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics — Find the Ising transition by Monte Carlo
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

The runs are long enough to settle, and that is shown.
T_c is extrapolated from the peak positions using T_c(L) − T_c ∝ 1/L, with an uncertainty from the fit.
Errors from correlated samples are handled.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.

Part of

Physics 11: Statistical Mechanics →

Related outcomes

Milestone map

3 milestones

Ensembles and the partition function

5 weeks (about 12 hrs/week)

Proof required

What gets checked

Each ensemble is chosen for a stated reason.
Thermodynamic quantities come from the partition function.
Review sets are marked against their solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.333 problem sets for these topics, then review sets 1–2, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics, unit 1: Ensembles and the partition function
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Each ensemble is chosen for a stated reason.
Thermodynamic quantities come from the partition function.
Review sets are marked against their solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Quantum gases and phase transitions

5 weeks (about 12 hrs/week)

Proof required

What gets checked

Bose and Fermi statistics are used where each applies.
Low-temperature limits are checked.
The review set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.333 problem sets for these topics, then review set 3, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics, unit 2: Quantum gases and phase transitions
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Bose and Fermi statistics are used where each applies.
Low-temperature limits are checked.
The review set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Find the Ising transition by Monte Carlo

5 weeks (about 12 hrs/week)

Proof required

Link the public repo with the notebook, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

The runs are long enough to settle, and that is shown.
T_c is extrapolated from the peak positions using T_c(L) − T_c ∝ 1/L, with an uncertainty from the fit.
Errors from correlated samples are handled.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A notebook that runs a Metropolis Monte Carlo simulation of the two-dimensional Ising model and estimates its critical temperature, in a public repo.

Steps

Write down what you expect before you start.
Measure the absolute magnetisation, susceptibility and heat capacity across temperatures for three lattice sizes, and compare with the exact value k_B·T_c = 2.269 J.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 11: Statistical Mechanics — Find the Ising transition by Monte Carlo
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

The runs are long enough to settle, and that is shown.
T_c is extrapolated from the peak positions using T_c(L) − T_c ∝ 1/L, with an uncertainty from the fit.
Errors from correlated samples are handled.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.