Symbol R_b
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
Take a system described by a set of couplings, coarse-grain it by integrating out the shortest-wavelength degrees of freedom, then rescale lengths so the cutoff returns to its original value. The result is a system of the same form with different couplings. Iterating defines a flow on the space of all possible Hamiltonians: . A critical point corresponds to a fixed point of this flow, a Hamiltonian that maps to itself, which is exactly the scale-invariance the diverging correlation length demanded. Linearising the map about the fixed point,
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Symbol K
K is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Equation 3 · Condensed Matter
More Is Different: Emergence and Phase Transitions
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Take a system described by a set of couplings, coarse-grain it by integrating out the shortest-wavelength degrees of freedom, then rescale lengths so the cutoff returns to its original value. The result is a system of the same form with different couplings. Iterating defines a flow on the space of all possible Hamiltonians: . A critical point corresponds to a fixed point of this flow, a Hamiltonian that maps to itself, which is exactly the scale-invariance the diverging correlation length demanded. Linearising the map about the fixed point,
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