The isotropic XY model on the inhomogeneous periodic chain
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS, 298 (2):
95-121 (2006)DOI: 10.1016/j.jmmm.2005.03.001
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.