Illustrated Physics
physics, drawn
Concept

Topological defect — where it appears

A point or line in a field at which some property cannot be defined continuously, held in place by a winding that cannot change by a small amount. Vortices in fluids and superfluids, phase singularities in light and dislocations in crystals are examples.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A stiffness that does not go to zero — it falls off a cliff. The renormalised stiffness of a two-dimensional superfluid against temperature, obtained by integrating the flow of the bare stiffness and the vortex fugacity, with the bare stiffness drawn for comparison. Below the transition the vortices are bound in pairs, screen one another and leave a finite stiffness; above it they unbind and there is none. What is remarkable is the value at which it disappears: 0.6430, against 2/π = 0.6366. That number does not depend on the material, on the bare fugacity, on the core energy, or on anything else — every two-dimensional superfluid loses its stiffness at exactly two over π times its own transition temperature, and measurements on helium films of widely different thicknesses fall on that line. A transition at which a quantity jumps to zero from a value nobody can adjust is unlike anything the usual classification of transitions describes.

The transition with nothing to order

Every transition in this collection so far has an order parameter — a quantity that is zero on one side and not on the other. In two dimensions a continuous symmetry cannot break at any temperature above zero, so there is nothing for such a quantity to be, and by the usual reckoning there can be no transition. There is one anyway, and what changes at it is whether vortices are bound in pairs.

thermodynamics · Phase change Three waves, and the points where the light is zero. The overlap of three equal plane waves travelling 120° apart: brightness (shading) and lines of equal phase every 60° (curves). Lines of every phase meet at isolated points where the brightness is exactly zero (dots); elsewhere only branches of a single phase cross, at the bright spots, where the phase is momentarily level. Round each such point the phase changes by one full turn, clockwise (red, charge +1) or anticlockwise (green, charge −1); in this window there are 18 of one and 18 of the other, arranged on a lattice in which every neighbour has the opposite sign. No adjustment of the phases removes them; shifting a wave only slides the lattice.

The dark lines a wave cannot avoid

Overlap three waves of light and there are places where they cancel exactly — not along fringes, as two waves cancel, but at isolated points, round which the phase of the light turns through a full circle. They cannot be removed by any small change, they can only be created or destroyed two at a time, and random light is full of them, about three to every square wavelength. A grating with a fork in it writes one into a beam on purpose, and the beam that comes out has a dark core and carries angular momentum in its twist.

optics · Diffraction

Named alongside it

The objects these essays reach for when they reach for this one.

Correlation functionCritical lineDiffraction gratingHologramInterferenceKosterlitz thoulessMermin wagnerOptical vortexOrbital angular momentumOrder parameterPhasePhase transition

All concepts