2011/08/31 by Aldo Isidori, Annika Ruppel, Andreas Kreisel +4 · 1 citation
Mathematics · Physics and Astronomy · #Antiferromagnetism #Condensed matter physics #Critical point (mathematics) #Density matrix renormalization group #Ferromagnetism #Heisenberg model #Ising model #Magnon #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Spin wave #Spins #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.84.184417
published as Phys. Rev. B 84, 184417 (2011) · 6 pages, 5 figures
openalex publication_date 2011/11/14 · arxiv created 2011/11/24 · arxiv updated 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory, the magnon dispersion for small momenta k is [\ensuremathΔ2+vk2k2]1/2, where \ensuremathΔ2\ensuremath∝|h\ensuremath-hc| and vk2\ensuremath∝|\phantom\rule-0.16em0exlnk|. For fields close to hc linear spin-wave theory breaks down, and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition and very broad on the disordered side.