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Physics of Particles and Nuclei

The correlation function and the thermodynamic quantities of the mixed system

Б. И. Садовников, Наталья Германовна Иноземцева, V. I. Inozemtsev

Published Nov 25, 2010• 2 citations
Publisher

Abstract

The themiodynamics of an in homogeneous 1D Heisenberg chain with alternating classical and quantum spins is studied. The explicit expressions for the free energy, specific heat, thermal spin correlations and linear susceptibility are found.
DOI
10.1134/s106377961007018x

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We consider thermodynamic properties, e.g. specific heat and magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry, these chains can be decomposed into a set of finite chain fragments. The problem of finding the thermodynamic quantities is effectively separated into two parts. First we deal with finite objects; secondly we can incorporate the fragments into a statistical ensemble. As functions of the coupling constants, the models exhibit special features in the thermodynamic quantities, e.g. the specific heat displays double peaks at low enough temperatures. These features stem from first-order quantum phase transitions at zero temperature, which have been investigated in the first part of this work.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
The exact solutions of the spin-spin correlation functions, the internal energy and the specific heat in a mixed spin Ising chain made up of two kinds of alternating magnetic atoms, namely spin-1/2 atoms and spin-S (S > 1/2) atoms with a crystal-field interaction constant D, are derived by the use of Ising spin identities and a differential operator technique. These solutions are valid for arbitrary values of S and D. Some numerical results are given for the specific heat. We find that the results exhibit characteristic behavior which does not follow the Schottky-type when the value of D becomes smaller than a (negative) critical value.