Critical phenomena

In physics, critical phenomena is the collective name associated with the physics of critical points.

Quotes

• The mathematical theory of critical phenomena is currently undergoing intense development. Intertwined with the science of phase transitions, it draws on ideas from probability theory and statistical physics.
  • Timothy Gowers; June Barrow-Green; Imre Leader (18 July 2010). The Princeton Companion to Mathematics. Princeton University Press. p. 657. ISBN 1-4008-3039-7. 
• [A]s a liquid changes into a gas at the critical temperature $T_{c}$, the heat capacity diverges as $c\sim {\frac {1}{\left|T-T_{c}\right|^{0.11008\ldots }}}$. The exponent is not known precisely. It is thought not to be a rational number, but should instead be viewed as a universal mathematical constant, similar to $\pi$ or $e$, but more subtle. Remarkably, the same exponent occurs for all gases. It also occurs in other systems, including a certain class of magnets. It's as if all knowledge of the microscopic physics has been washed away, leaving us with something pure, that carries only a vague memory of what lies underneath. This phenomenon is known as universality... In our attempt to understand what happens as water boils, we will need to develop new tools and a new way of thinking about the world. This leads us to a paradigm which now underlies huge swathes of physics, far removed from its humble origin of a pot on a stove. This paradigm revolves around two deep facts about the Universe we inhabit: Nature is organised by symmetry. And Nature is organised by scale.
  • David Tong: Lectures on Statistical Field Theory, 2017.