Equation 2 · Part 6 · More Is Different: Emergence and Phase Transitions
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
Approaching a continuous transition, correlations between distant parts of the system grow. Away from the critical temperature there is a finite correlation length, the size of a typical patch that acts as a unit. As the reduced temperature goes to zero, that length diverges: . At the critical point itself, the only lengths remaining in the problem are the microscopic cutoff, meaning the lattice spacing or molecular size, and the size of the sample. Everything in between is populated: fluctuating regions of every intermediate scale coexist, each a smaller copy of the pattern above it. In a fluid near its critical point this is directly visible, as the density fluctuations…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
The article lists its research sources here.