  In conformal field theory, key properties of spin-1/2 chains, such as the
ground state energy per site and the excitation gap scale with dimerization
delta as delta^alpha with known exponents alpha and logarithmic corrections.
The logarithmic corrections vanish in a spin chain with nearest (J=1) and next
nearest neighbor interactions (J_2), for J_2c=0.2411. DMRG analysis of a
frustrated spin chain with no logarithmic corrections yields the field
theoretic values of alpha, and the scaling relation is valid up to the
physically realized range, delta ~ 0.1. However, chains with logarithmic
corrections (J_2<0.2411 J) are more accurately fit by simple power laws with
different exponents for physically realized dimerizations. We show the
exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from
approximately 3/2 to 4/3 for the energy per site and error bars in the exponent
also decrease as J_2 approaches to J_2c.
