Article,
The longitudinal dynamic correlation and dynamic susceptibility of the isotropic XY-model on the 1D alternating superlattice
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 311 (3-4): 458-474 (2002)
DOI: 10.1016/S0378-4371(02)00826-9
Abstract
The dynamic susceptibility Z(Q)(zz) (omega) of the isotropic XY-model (s = 1/2) on the alternating superlattice (closed chain) in a transverse
field h is obtained exactly at arbitrary temperatures. It is determined
from the results obtained for the dynamic correlations
<S-j,n(z)(t)S-l,S-m(0)>, which have been calculated by introducing the
generalized Jordan-Wigner transformation, by using Wick's theorem and by
reducing the problem to a diagonalization of a finite matrix. The static
properties are also reobtained within this new formalism and all exact
results are determined for arbitrary temperatures. Explicit results are obtained numerically in the limit T = 0, where the critical behaviour
occurs. A detailed analysis is presented for the behaviour of the static
susceptibility Z(Q)(zz)(0), as a function of the transverse field h, and
for the frequency dependency of the dynamic susceptibility
Z(Q)(zz)(omega). It is also shown, in this temperature limit, that
within the magnetization plateaus which correspond to the different
phases, even when the induced magnetization is not saturated, the
effective dynamic correlation, <Sigma(n,mis an element ofcell:j:l)
S-j,n(z)(t)S-l,m(z)(0)>, is time independent, which constitutes an
unexpected result. (C) 2002 Elsevier Science B.V. All rights reserved.
