2007/01/31 by J.P. de Lima, J. P. de Lima, L.L. Gonçalves +2 · 2 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.75.214406
33 pages, 13 figures, 01 table. Revised version (minor corrections) accepted for publiction in Phys. Rev. B
arxiv created 2007/04/09 · openalex publication_date 2007/06/05 · arxiv updated 2009/12/01 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/28
The static and dynamic properties of the anisotropic XY model (s=1∕2) on the inhomogeneous periodic chain, composed of N cells with n different exchange interactions and magnetic moments, in a transverse field h, are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of nth order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization 1∕n\ensuremath∑m=1n\ensuremathμm⟨Sj,mz⟩ (j denotes the cell, m the site within the cell, \ensuremathμm the magnetic moment at site m within the cell) and the spontaneous magnetization 1∕n\ensuremath∑m=1n⟨S_j,m^\ensuremath'x⟩ which is obtained from the correlations ⟨Sj,mxSj+r,mx⟩ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong [Physica B 304, 91 (2001)]. The dynamic correlations, ⟨Sj,mz(t)S_j^\ensuremath',m^\ensuremath'z(0)⟩, and the dynamic susceptibility, \ensuremathχqzz(\ensuremathω), are also obtained at arbitrary temperatures. Explicit results are presented in the limit T=0, where the critical behavior occurs, for the static susceptibility \ensuremathχqzz(0) as a function of the transverse field h, and for the frequency dependency of dynamic susceptibility \ensuremathχqzz(\ensuremathω).