Equation 2 · Part 11 · More Is Different: Emergence and Phase Transitions
Numerator: T - T_c
What this part means
The complete quantity above the fraction bar.
Its job in the formula
T - occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: T - T_c→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
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
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