Second-order transition

Definition

A second-order transition is a phase transition that occurs without a discontinuity in the first derivative of the free energy, such as entropy or volume, but exhibits a discontinuity in the second derivative, such as heat capacity or compressibility. These transitions typically happen at critical points and are characterized by changes in symmetry and fluctuations that can lead to critical phenomena, connecting directly to concepts of phase equilibria and stability.

5 Must Know Facts For Your Next Test

1. Second-order transitions are often associated with continuous symmetry breaking, meaning that the system changes from a symmetric state to one that has a distinct order.
2. The heat capacity of materials usually shows a peak at second-order transitions due to critical fluctuations occurring as the system approaches the transition temperature.
3. Examples of second-order transitions include the ferromagnetic transition at the Curie temperature and the superfluid transition in helium-4.
4. Second-order transitions do not involve latent heat, which is why they are characterized by smooth changes rather than abrupt ones.
5. Fluctuations become increasingly important near second-order transitions, leading to phenomena such as scaling and universality in critical behavior.

Review Questions

• How do second-order transitions differ from first-order transitions in terms of thermodynamic properties?
  • Second-order transitions differ from first-order transitions primarily in their thermodynamic properties. While first-order transitions feature discontinuities in the first derivatives of free energy, such as volume and entropy, second-order transitions exhibit continuity in these derivatives but show discontinuities in their second derivatives, like heat capacity. This distinction highlights how second-order transitions represent more subtle shifts in state without abrupt changes in energy requirements.
• Discuss the significance of critical points in relation to second-order transitions and their implications for phase equilibria.
  • Critical points play a vital role in understanding second-order transitions as they mark the conditions under which different phases coexist and exhibit unique behavior. At these points, materials display significant changes in properties due to fluctuations that become dominant. This relationship underscores how second-order transitions provide insights into phase equilibria by highlighting regions where multiple phases interact closely and influence stability.
• Evaluate how fluctuations near second-order transitions lead to critical phenomena and what this means for material properties.
  • Fluctuations near second-order transitions can result in critical phenomena that profoundly affect material properties, such as enhanced susceptibility and changes in conductivity. As systems approach these transitions, they experience collective behavior that can amplify these fluctuations. This collective nature leads to emergent properties that are not present at other temperatures or phases, making second-order transitions crucial for understanding complex systems in both theoretical and practical contexts.

Related terms

First-order transition: A phase transition where there is a discontinuity in the first derivative of the free energy, typically accompanied by latent heat.

Critical point: The end point of a phase equilibrium curve, where distinct liquid and gas phases cease to exist and properties exhibit divergent behavior.

Order parameter: A quantity that measures the degree of order across a phase transition, often used to characterize the nature of transitions.