The correlation function and the thermodynamic quantities of the mixed system
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ESSION “STATISTICAL MECHANICS, KINETICS AND QUANTUM THEORY OF CONDENSED MATTER”
The Correlation Function and the Thermodynamic Quantities of the Mixed System1 B. I. Sadovnikova, N. G. Inozemtsevab, and V. I. Inozemtsevc a
Department of Physics, Moscow State University b Dubna International University cBLTP JINR, Dubna, Moscow Region, 141980 Russia 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 1
The Heisenberg spin lattices have been extensively studied throughout many years as simplest models for magnetic phenomena. Motivated by the famous Bethe solution in 1D [1], a number of theoretical and exper imental investigations of quantum spin chains with nearestneighbor interaction has been performed in the last thirty years by using exact Bethe ansatz [2, 3], high and lowtemperature expansions [4] and renor malization group calculations [5, 6]. In the meantime, attention has been paid also to the classical version of the model in which spins are represented by unit vec tors located on the sites of 1D lattice for both cases of periodic [7, 8] and open boundary conditions [9]. In comparison to the overcomplicated form of the solu tion to the quantum systems, the classical results look rather simple and allow one to read the expressions for thermodynamic quantities explicitly in the absence of a magnetic field [7–9].
In various situations which now can be realized in magnetic substances, the arrangement of spins might be quite different, either from classical or pure quan tum situation. The lattice structure of chemical com pounds can comprise magnetic ions with spins of dif ferent magnitudes arranged periodically [10] in a fam ily of quasionedimensional chains. In the limit of weak interchain coupling, one can approximate the system by noninteracting 1D chains with nearest neighbor interaction of different spins (say, spins 1/2 on even sites and spin 5/2 on odd ones). These two interacting sublattices are very different and the result ing quantum chain is not integrable. However, one could introduce classical spins instead of the spins of higher magnitude which makes the chain more tracta ble. In this case, taking the trace with respect to quan tum and classical degrees of freedom can be performed separately which leads to analytic result in the absence of magnetic field.
The aim of this note is to find explicit expression for the thermodynamic quantities of these mixed classi calquant urn chains in 1D, and to calculate its linear susceptibility. The starting point is the Hamiltonian of the finite lattice of the form J HN = 2
N
∑ (n
2j – 1 σ 2j
+ σ 2j n 2j + 1 ),
(1)
j=1
2
where n 2j – 1 ( n 2j – 1 = 1) are the vectors of classical spins located on odd sites of the lattice and σ 2j are Pauli matrices representing quantum s = 1/2 spins located on even sites. We
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