% miko:type: atomic
% miko:title: Phase Transition
% miko:summary: A nonanalytic change in equilibrium behavior as control parameters vary.
% miko:tags: thermo
% miko:difficulty: undergrad
% miko:related: clausius-clapeyron-equation, gibbs-free-energy, ising-model
% miko:keywords: order parameter, latent heat, critical point

\documentclass{article}
\usepackage{amsmath}
\title{Phase Transition}
\begin{document}
\maketitle

\section{Definition}

A phase transition occurs when thermodynamic properties change
nonanalytically in the thermodynamic limit. First-order transitions have a
discontinuity in a first derivative of a thermodynamic potential and often
involve latent heat.

\section{Order Parameters}

An order parameter distinguishes phases. Magnetization in a ferromagnet and
density difference in a liquid-gas transition are standard examples.

\section{Criticality}

At a continuous transition, correlation lengths can become large compared with
microscopic scales. This is why very different systems can share universal
critical behavior.

\end{document}
