---
title: "Phase Transitions, Order Parameters and Broken Symmetry"
description: "A phase transition appears as a point where the free energy stops being smooth, and an order parameter measures which symmetry the ordered phase has given up. First-order and continuous transitions di"
canonical: https://lightmysky.com/learn/science/phase-transitions-order-parameters-and-broken-symmetry-mt_3DQjfNJ-Ef
source: https://lightmysky.com/learn/science/phase-transitions-order-parameters-and-broken-symmetry-mt_3DQjfNJ-Ef.md
retrieved: 2026-09-12
---

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# Phase Transitions, Order Parameters and Broken Symmetry

A phase transition appears as a point where the free energy stops being smooth, and an order parameter measures which symmetry the ordered phase has given up. First-order and continuous transitions differ in whether that parameter jumps.

Subject: Science · Area: Thermal & Statistical Physics · Ages 22 to 24
Page: https://lightmysky.com/learn/science/phase-transitions-order-parameters-and-broken-symmetry-mt_3DQjfNJ-Ef

## Ready when they can

- Chooses an order parameter for a named transition and says what it measures
- Separates first-order from continuous transitions by the behaviour of free energy derivatives
- Explains which symmetry the ordered phase breaks and why the disordered one has it

## Lesson: Order appears, symmetry goes

A phase transition is a kink in the free energy: some derivative jumps or blows up at the point. The order parameter measures the new order directly: zero in the disordered phase, nonzero where the system picked an alignment.

**Example.** Take a magnet, whose order parameter is magnetization. Hot, it reads zero: spins point everywhere and full rotation symmetry holds. Cold, it turns nonzero: spins pick a direction, and the state keeps less symmetry than the laws behind it.

First-order and continuous transitions differ at the point. First-order jumps: the parameter leaps and latent heat flows. Continuous grows smoothly from zero with diverging derivatives and no latent heat. Watch the parameter cross the point and you know which you saw.

**Tip.** Name the broken symmetry, not just the phase: rotation symmetry broken by magnetization says more than it became magnetic. The parameter tells you exactly which symmetry gave way.

**Recap.** Kinked free energy, a parameter that wakes up, and a symmetry left behind.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Fluctuations, Linear Response and the Fluctuation-Dissipation Relation](https://lightmysky.com/learn/science/fluctuations-linear-response-and-the-fluctuation-dissipation-relation-mt_Ibsvdyx7uP)
- [Noether's Theorem: Symmetry and Conserved Quantities](https://lightmysky.com/learn/science/noethers-theorem-symmetry-and-conserved-quantities-mt_kAoOn8syBK)

## Opens up

- [The Ising Model and the Mean-Field Approximation](https://lightmysky.com/learn/science/the-ising-model-and-the-mean-field-approximation-mt_wPwyBTVI0C)