# Phase Transitions & Critical Phenomena

Canonical: https://manyspace.aporia.systems/topics/phase-transitions-critical-phenomena-phy-statm-103
Updated: 2026-10-13

Physics · Statistical Mechanics · PHY-STATM-103

- Difficulty: 4 / 5
- Importance: 4 / 5
- Study time: 6.5–11.5 h

order parameters, Landau theory, Ising model, universality

## Why it matters

Derives macroscopic thermodynamics from microscopic dynamics of many particles; central to condensed matter, chemistry and beyond.

## Where it is used

Materials science, semiconductor physics, engines, stellar structure, biological systems, information thermodynamics.

## How you know you have learned it

Explain/derive key result from memory + solve 2 non-routine checks.

## What you need first

- [Temperature & Thermal Equilibrium](https://manyspace.aporia.systems/topics/temperature-thermal-equilibrium-phy-thermo-043) (required)
- [Sample Spaces & Events](https://manyspace.aporia.systems/topics/sample-spaces-events-mth-prob-196) (helpful)
- [Center of Mass & Rigid Body Motion](https://manyspace.aporia.systems/topics/center-of-mass-rigid-body-motion-phy-mech2-084) (helpful)

## Resources

- Statistical Physics of Particles — Mehran Kardar
- Statistical Physics of Particles — Mehran Kardar
- Statistical Mechanics — R. K. Pathria