2020/09/07 by Max A. Metlitski, Metlitski, Max A. · 11 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2009.05119
openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. For the ordinary transition the bulk and the boundary order simultaneously; the extra-ordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N ≥ 2. Here we show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. In particular, for N=2, starting in the surface phase with quasi-long-range order and approaching the bulk phase transition, the stiffness of the surface order parameter diverges logarithmically. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law; we discuss two scenarios for the evolution of the phase diagram past N = Nc. Our findings appear to be consistent with recent Monte-Carlo studies of classical models with N = 2 and N = 3. We also compare our results to numerical studies of boundary criticality in 2+1D quantum spin models.