2004/09/22 by Ar. Abanov, Andrey V. Chubukov, Abanov, Ar. +2
Earth and Planetary Sciences · Physics and Astronomy · #Earthquake Detection and Analysis #FOS: Physical sciences #Quantum, superfluid, helium dynamics #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0409601
4 pages, 3 figures
arxiv created 2004/09/22 · openalex publication_date 2004/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that Hertz ϕ4 theory of quantum criticality is incomplete as it misses anomalous non-local contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d= 4-z =2, however the number of marginal vertices at d=2 is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for d<2 the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains z=2.