%0 Journal Article %1 WOS:000233704100004 %A de Lima, JP %A Alves, TFA %A Goncalves, LL %C PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS %D 2006 %I ELSEVIER SCIENCE BV %J JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS %K chain} inhomogeneous model; quantum transition; {XY %N 2 %P 95-121 %R 10.1016/j.jmmm.2005.03.001 %T The isotropic XY model on the inhomogeneous periodic chain %V 298 %X The static and dynamic properties of the isotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N segments with n different exchange interactions and magnetic moments, in a transverse field 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 nth 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) Sigma(n)(m=1) mu(m) S-j,m(z) where mu(m) is the magnetic moment at site in within the segment j, as a function of the field, and the critical fields determined exactly. The dynamic correlations, S-j,m(z)(t)S-j,m(z) (0), and the dynamic susceptibility chi(zz)(q)(omega) are also obtained at arbitrary temperatures. Explicit results are presented in the limit T = 0, where the critical behaviour occurs, for the static susceptibility chi(zz)(q)(0) as a function of the transverse field h, and for the frequency dependency of dynamic,q susceptibility chi(zz)(q)(omega). Also in this limit, the transverse time-correlation (S-j,m(x)(t)S-j,m'(x)(0)) and the dynamic and isothermal susceptibilities, chi(xx)(q)(omega) and chi(xx)(T), are obtained for the transverse field greater or equal than the saturation field. (C) 2005 Elsevier B.V. All rights reserved.

@article{WOS:000233704100004, abstract = {The static and dynamic properties of the isotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N segments with n different exchange interactions and magnetic moments, in a transverse field 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 nth 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) Sigma(n)(m=1) mu(m) [S-j,m(z)] where mu(m) is the magnetic moment at site in within the segment j, as a function of the field, and the critical fields determined exactly. The dynamic correlations, [S-j,m(z)(t)S-j,m(z) (0)], and the dynamic susceptibility chi(zz)(q)(omega) are also obtained at arbitrary temperatures. Explicit results are presented in the limit T = 0, where the critical behaviour occurs, for the static susceptibility chi(zz)(q)(0) as a function of the transverse field h, and for the frequency dependency of dynamic,q susceptibility chi(zz)(q)(omega). Also in this limit, the transverse time-correlation (S-j,m(x)(t)S-j,m'(x)(0)) and the dynamic and isothermal susceptibilities, chi(xx)(q)(omega) and chi(xx)(T), are obtained for the transverse field greater or equal than the saturation field. (C) 2005 Elsevier B.V. All rights reserved.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}, author = {de Lima, JP and Alves, TFA and Goncalves, LL}, biburl = {https://www.bibsonomy.org/bibtex/2a881c07206c6b2d74ab2b56676e31509/ppgfis_ufc_br}, doi = {10.1016/j.jmmm.2005.03.001}, interhash = {6ea3c2c4b2040c85f4d2bca272b03ac9}, intrahash = {a881c07206c6b2d74ab2b56676e31509}, issn = {0304-8853}, journal = {JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS}, keywords = {chain} inhomogeneous model; quantum transition; {XY}, number = 2, pages = {95-121}, publisher = {ELSEVIER SCIENCE BV}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {The isotropic XY model on the inhomogeneous periodic chain}, tppubtype = {article}, volume = 298, year = 2006 }