2003/07/01 by Alexander G. Abanov, Fabio Franchini · 2 citations
Mathematics · Physics and Astronomy · #Classical XY model #Condensed matter physics #Critical exponent #Exponent #Exponential function #Ferromagnetism #Gaussian #Heisenberg model #Isotropy #Magnetic field #Mathematical analysis #Mathematics #Phase transition #Physics #Power law #Quantum many-body systems #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #String (physics) #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2003.07.009
published as Phys.Lett. A316 (2003) 342-349 · 15 pages, 3 figures, elsart document class
arxiv created 2003/07/01 · openalex publication_date 2003/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length "n" in a ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n goes to infinity. We find that it is exponential everywhere in the phase diagram of the XY model except at the critical lines where the spectrum is gapless. One of those lines corresponds to the isotropic XY model where EFP decays in a Gaussian way, as was shown in cond-mat/0106062. The other line is at the critical value of the magnetic field. There, we show that EFP is still exponential but acquires a non-trivial power-law prefactor with a universal exponent.