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Acta Physica Polonica A

Transfer-Matrix Simulations of Linear Magnetic Systems

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

Published May 1, 2000• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.97.959

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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.
The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable su(3)su(3)su(3) model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-111 chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat, and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds Ni(C2H8N2)2Ni(CN)4{\mathrm{Ni}(\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}Ni(C2​H8​N2​)2​Ni(CN)4​ and ${\mathrm{Ni}(\mathrm{C}}_{10}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$.
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.