Boundary RG and QMC show log corrections control ordinary and special surface transitions of a (3+1)D O(3) quantum critical point, with hat-coppa finite-size forms.

Summary. The manuscript studies logarithmic corrections to bulk and surface criticality at a (3+1)D O(3) quantum critical point of a Heisenberg antiferromagnet, i.e., at the bulk upper critical dimension. Combining large-scale quantum Monte Carlo with boundary renormalization-group analysis, it first recovers the known logarithmically modified bulk finite-size scaling, including correlation-length scaling controlled by the logarithmic finite-size exponent hat-coppa. Surface coupling is then tuned to identify ordinary, special, and extraordinary boundary regimes. For ordinary and special transitions the authors derive logarithmic correction exponents and hat-coppa-dependent finite-size scaling forms for boundary correlations (including forms claimed not to have been systematically established before) and report quantitative support from QMC. In the extraordinary regime they report long-range surface magnetic order together with a logarithmically enhanced surface-bulk correlation.

Significance. Multiplicative logarithmic corrections at the upper critical dimension are well developed for bulk observables but much less so for boundary criticality and finite-size scaling. If the derived hat-coppa-dependent surface scaling forms and the extraordinary-regime findings hold under quantitative scrutiny, the work would systematically extend the upper-critical-dimension program to surfaces and supply concrete, falsifiable scaling predictions for simulations and experiments. The architecture—independent boundary RG predictions tested against large-scale QMC, with bulk logarithmic scaling verified first as a control—is methodologically sound in design and, if the data and derivations check out, constitutes a clear advance for surface criticality in O(3) systems.