L. S. Campana

Static properties of quantum spin S=1 chains: TMNB, TMNC and CsNiF3

The zero-field parallel and perpendicular susceptibility and the zero-field specific heat of the quantum easy-plane S=1 Heisenberg spin chains are calculated numerically and applied to TMNB, TMNC and CsNiF3. New values of the model parameters are estimated from fitting procedures. As to CsNiF3, the in-plane specific heat, the field-dependent magnetization and the spin-wave dispersion are also evaluated for a given choice of the microscopic parameters (J/kB=20.5 K, A/J=0.425) and compared with measured quantities. An overall agreement with experiment is revealed.

A proposal to include damping effects in the spectral density approach

Recently there has been proposed a modification of the spectral density method (SDM) to take into account damping effects for Fermi systems. There are in any case some difficulties concerning Bose and classical systems. The authors suggest a simple way of avoiding such difficulties and preserving the earliest idea for discussing damping effects. A classical ferromagnetic linear chain in external magnetic field is studied.

Callen-like method for the classical Heisenberg ferromagnet

A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function’s framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest.

Spectral density approach for the damping of fermion elementary excitations in an anisotropic spin-12 linear chain

The paper is devoted to an investigation of the damping effects of the Fermion elementary excitations in the Jordan-Wigner representation of a one-dimensional anisotropic spin-12 model in an external field. This is realized on the basis of the “Gaussian ansatz”, recently proposed by Nolting and Oles, as substituting the standard “polar ansatz” in the Spectral Density Method, for exploring damping effects of quasi-particles in many-body problems. By using a first order approximation, we are able to obtain reasonable results in the low temperature limit.

Finite chain results for the magnetization and specific heat of CsNiF3

Abstract Numerical calculations for the magnetization and the specific heat of CsNiF3 are performed by using finite chains with size N⩽7 and the linear extrapolation procedure for 1/N→0. Except for the lowest temperatures, the theoretical estimates are consistent with the magnetization measurements. Fairly good agreement is also found for the maxima in the excess specific heat but their positions are underestimated.

Spectral density method for an anisotropic linear chain

The spectral density method is used to study the thermodynamic properties of an anisotropic antiferromagnetic Heisenberg linear chain in an external magnetic field. Insecond order approximation without the decoupling procedure for the two particle correlation function, we are able to obtain many results in terms of both the temperature and the magnetic field for different values of the anisotropy parameter. The ground state of the model is investigated and the singular behaviour of some thermodynamic quantities near the critical field is determined. In particular, explicit analytical solutions are given for small anisotropy parameters. Our results are compared with the ones obtained by means of other methods and some exact results are reproduced.

Low-temperature behaviour of a high-density Bose model

SummaryThe low-temperature thermodynamic properties of a high-density Bose gas with strong attraction between the particles are obtained within the Bogolubov approximation. An approach is used which also gives an interesting connection between the Bogoliubov approximation and the spectral-density method.RiassuntoAdoperando l’approssimazione di Bogoliubov, si studiano le proprietà termodinamiche, nella regione di basse temperature, di un gas di Bose ad alta densità con attrazione forte tra le particelle. Noi usiamo un procedimento che fornisce anche un’interessante connessione tra la suddetta approssimazione e il metodo della densità spettrale.РезюмеВ рамках приближения Боголюбова исследуются термодинамические свойства при низких температурах Бозе-газа с высокой плотностью и с сильным притяжением между частицами. Используется подход, который дает интересную связь между приближением Боголюбова и методом спектральной плотности.

On the spectral-density approach to the correlation functions of a linear magnetic model

SummaryWe show that, when one uses the spectral-density method (SDM) to study the spin-spin correlation functions for a Heisenberg linear chain, a difficulty appears in a simple procedure usually utilized to avoid the decoupling in the higher spectral density. Such a difficulty does not exist at the first and second order in the SDM with the decoupling procedure. In these approximations the correlation functions are obtained for arbitrary values of the temperature, the magnetic field and the anisotropy parameter.RiassuntoQuando si usa il metodo delle densità spettrali per lo studio delle funzioni di correlazione spin-spin per una catena lineare di Heisenberg, appare una difficoltà nel procedimento usualmente utilizzato per evitare il disaceoppiamento nella densità spettrali di ordine più elevato. Una tale difficoltà non interviene al primo e al secondo ordine nell–MSD con il procedimento di disaccoppiamento. In tali approssimazioni le funzioni di correlazione sono ottenute per arbitrari valori della temperatura, del campo magnetico o del parametro di anisotropia.РезюмеМы показываем, что при использовании метода спектральной плотности для исследования спин-спиновых корреляционных функций для линейной цепочки Гайзенберга возникает трудность при применении простой процедуры, позволяющей избежать нарушения связи при высокой спектральной плотности. Указанная трудность не возникает в первом и во втором порядках в методе спектральной плотности. В этих приближениях получаются корреляционные функции для произвольных значений температуры, магнитного поля и параметра анизотропии.

Thermodynamic properties of some S = 1 soliton-bearing and Haldane-like systems

Abstract The numerical finite-size technique has been applied to study thermodynamic properties of the S = 1 quasi-one-dimensional magnets CsNiF 3 , (CH 3 ) 4 NNiBr 3 (TMNB), (CH 3 ) 4 NNiCl 3 (TMNC) and CsNiCl 3 , the latter showing the Haldane gap. The length of chains has been extended up to N ≤ 8 and the successful fitting procedure has been performed to match the parameters of the easy-plane Heisenberg model with single-ion anisotropy. The quantitative agreement with experiment has been found both for the zero-field and the field-dependent properties. An attempt to apply the renormalization-group approach is also put forward for CsNiCl 3 .

A position-space study of the anisotropic quantum Ising model

A global real-space renormalisation group method is applied to the transverse Ising model on an anisotropic square lattice. Recursion relations with non-trivial isotropic fixed points at zero and finite temperature are found in agreement with the universality hypothesis. The critical field as a function of the anisotropy at T=0 and the critical temperature as a function of the field for different values of the anisotropy parameters are calculated.