2006/10/04 by D. V. Dmitriev, Д. В. Дмитриев, V. Ya. Krivnov +2 · 1 citation
Mathematics · Physics and Astronomy · #Antiferromagnetism #Condensed matter physics #Critical exponent #Critical point (mathematics) #Excited state #Exponent #Ferromagnetism #Geometry #Ground state #Heisenberg model #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Scaling #Singlet state #Spin (aerodynamics) #Theoretical and Computational Physics #Thermodynamics #Transition point #Zigzag #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.75.014424
published as Phys. Rev. B75, 014424 (2007) · 13 pages, 3 figures
arxiv created 2006/10/04 · openalex publication_date 2007/01/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The properties of the ferromagnetic frustrated spin-S one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for s=1∕2 are sufficiently strong to change the classical critical exponents, while for spin systems with s\ensuremath\geqslant1 the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.