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Acta Physica Polonica A

Numerical Simulations of Linear S=1 Ferro- and Antiferromagnets

G. Kamieniarz, R. Matysiak, Alvaro Caramico D’Auria, Francesco Esposito, Ugo Esposito

Published Aug 1, 1997• 1 citation
Publisher

Abstract

Tle finite-temperature static properties of the spin S 1 antiferromag- netic Heisenberg chains are extensively simulated using the quantum transfer matrix method.The zero-field susceptibility and specific heat as well as the field-dependent magnetization data are evaluated to select the microscopic parameters of a number of real quasi-one-dimensional compounds and to verify some theoretical approaches.

DOI
10.12693/aphyspola.92.387

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Tle finite-temperature static properties of the spin S 1 antiferromag- netic Heisenberg chains are extensively simulated using the quantum transfer matrix method.The zero-field susceptibility and specific heat as well as the field-dependent magnetization data are evaluated to select the microscopic parameters of a number of real quasi-one-dimensional compounds and to verify some theoretical approaches.
The quantum transfer-matrix method was applied to study the finite--temperature static properties of the spin S = 1 antiferromagnetic Heisen- berg chains in a wide range of the single-ion anisotropy and temperatures.The high-resolution quantum transfer-matrix simulation data are obtained for the zero-field susceptibility, specific heat as well as for the field-dependent magnetization.The microscopic parameters of a number of real quasi-one--dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and an extension of the technique to a non-uniform bond alternating molecular magnets is ałso put forward.
The quantum transfer-matrix method (QTM) has been applied to study the finite-temperature static properties of the spin S=1S=1S=1 antiferromagnetic Heisenberg chains in a wide range of the single-ion anisotropy and temperatures. The high-resolution QTM simulation data are obtained for the zero-field susceptibility, specific heat, as well as for the field-dependent magnetization. The microscopic parameters of a number of real quasi-one-dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and low-temperature extensions of high-temperature series are given in terms of Chebyshev polynomials.
By the numerical transfer-matrix method we have computed several thermal properties for a Heisenberg chain of 150 antiferromagnetically coupled spins with quantum number s = 1. We dispensed with any extrapolation to the infinite chain, because the results for the magnetization, the susceptibility, the correlation length, and the static structure factor at wave number q = π have been found to be insensitive to a further increase of the chain length in the temperature regime considered. The characteristic features of our results, that occur at sufficiently low temperatures and low applied fields, can convincingly be explained by the existence of a gap in the excitation spectrum of the order of 0.4 coupling constants and, therefore, nicely complement previous numerical results for corresponding ground-state properties. We have also performed computations for a chain with an additional single-site anisotropy. We find, for appropriate parameter values, excellent agreement with experimental data for the quasi-one-dimensional model compound NENP.
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 one-dimensional quantum Heisenberg model with random \ifmmode\pm\else\textpm\fi{}J bonds is studied for S=1/2 and S=1. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and the quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite-size systems.