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The isotropic XY model on the inhomogeneous periodic chain | | J. P de Lima
; T. F. A. Alves
; L. L. Goncalves
; | | Date: |
21 Dec 2004 | | Subject: | Statistical Mechanics; Materials Science | cond-mat.stat-mech cond-mat.mtrl-sci | | Abstract: | The static and dynamic properties of the isotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of emph{N} segments with emph{n} different exchange interactions and magnetic moments, in a transverse field emph{h} are obtained exactly at arbitrary temperatures. The properties are determined by introducing the generalized Jordan-Wigner transformation and by reducing the problem to a diagonalization of a finite matrix of emph{n-th} order. The diagonalization procedure is discussed in detail and the critical behaviour induced by the transverse field, at T=0, is presented. The quantum transitions are determined by analyzing the behaviour of the induced magnetization, defined as $(1/n)sum_{m=1}^{n}mu_{m}$ where $mu_{m}$ is the magnetic moment at site emph{m} within the segment emph{j}, as a function of the field, and the critical fields determined exactly. The dynamic correlations, $$, and the dynamic susceptibility $chi_{q}^{zz}(omega)$ are also obtained at arbitrary temperatures. Explicit results are also presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility $chi_{q}^{zz}(0)$ as a function of the transverse field emph{h}, and for the frequency dependency of dynamic susceptibility $chi_{q}^{zz}(omega)$. Also in this limit, the transverse time-correlation $$, the dynamic and isothermal susceptibilities, $chi_{q}^{xx}(omega)$ and $chi_{T}^{xx}$, are obtained for the transverse field greater or equal than the saturation field. | | Source: | arXiv, cond-mat/0501525 | | Services: | Forum | Review | PDF | Favorites | |
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