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Annual Conference on Magnetism and Magnetic Materials (MMM)

The Ising Model with a Transverse Field

Yung‐Li Wang, James W. Johnson

Published Jan 1, 1974• 3 citations
Publisher

Abstract

The Ising Model in a transverse field is investigated employing a field theoretical diagrammatic technique. The diagrams are classified with respect to a high density parameter 1/z, where z is the number of spins interacting with a given spin. The energy spectrum of collective excitations has been obtained both in the disordered phase and in the ordered phase. Summation of the chain diagrams (of order 1) reproduces the previous results. We have calculated the contributions of all diagrams of order 1/z and showed that the RPA commonly used has failed to include consistently a class of diagrams which reflect the kinematics of spin operators. The damping of the excitation waves is also obtained.

DOI
10.1063/1.2947271

Related papers

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CPA approach to the random Ising model in a transverse field

Peter Prelovšek, R. Pirc

The dynamics of a two-component Ising model in a transverse field (IMTF) with randomness during both in the transverse field and the Ising coupling is treated within the single-site coherent potential approximation (CPA). The authors deal primarily with the polarized phase; they replace the fluctuating longitudinal component of the molecular field by two effective parameters, one for each species, which are determined self-consistently. The CPA spectra of the collective spin excitations are found analytically in the dilute case using a Hubbard model density for the Ising interaction, and are also calculated numerically for the general two-component IMTF. It is shown that the static susceptibility cannot diverge within the single site CPA. Characterizing the phase transition by the softening of the lowest mode in the spectrum. The stability conditions for the polarized phase at T=O are then determined.

Journal of Physics C Solid State Physics•Mar 28, 1977•16 citations
The Ising Model in a transverse field is investigated employing a field theoretical diagrammatic technique. The diagrams are classified with respect to a high density parameter 1/z, where z is the number of spins interacting with a given spin. The energy spectrum of collective excitations has been obtained both in the disordered phase and in the ordered phase. Summation of the chain diagrams (of order 1) reproduces the previous results. We have calculated the contributions of all diagrams of order 1/z and showed that the RPA commonly used has failed to include consistently a class of diagrams which reflect the kinematics of spin operators. The damping of the excitation waves is also obtained.
For Pt. I see ibid., vol. 6, no. 15, 2459 (1973). By taking the (1/z) expansion one order beyond that considered in Pt. I, a detailed discussion is provided of the generalized susceptibilities and spectral functions rho alpha beta of the Ising model in a transverse field Gamma . The leading contributions to the damping of the excitations as well as the first-order shift in their energy and in the critical temperature, are obtained. The damping arises from break-up into (i) a spin wave and a spin fluctuation or (ii) a pair of spin waves.
An Ising model in a transverse field with general spin S is considered within RPA Green-function theory in the paramagnetic region. Expressions for the temperature renormalised collective excitation spectrum with a gap decreasing as the exchange interaction increases, the transverse correlation function, and the critical exchange-field ratio for magnetic ordering, are derived. Zero-temperature expansions are given in the limit of weak interaction. Critical values at T=0K are calculated for several values of S and an asymptotical expression for S>>1 is given.
We study the phase diagram and magnetic properties of a transverse spin-1 Ising model with random longitudinal crystal-field interactions using an expansion technique for cluster identities of spin-1 localized spin systems. Partially ordered phases appear for a particular two valued distribution P(D i )=1/2( delta (D i -(1+ alpha )D)+ delta (D i -(1- alpha )D)), and sufficiently small transverse field Omega . The longitudinal and transverse magnetizations and the quadrupolar moments are calculated. General formulae, applicable to structures with arbitrary coordination number N, are given.
The dynamics of a two-component Ising model in a transverse field (IMTF) with randomness during both in the transverse field and the Ising coupling is treated within the single-site coherent potential approximation (CPA). The authors deal primarily with the polarized phase; they replace the fluctuating longitudinal component of the molecular field by two effective parameters, one for each species, which are determined self-consistently. The CPA spectra of the collective spin excitations are found analytically in the dilute case using a Hubbard model density for the Ising interaction, and are also calculated numerically for the general two-component IMTF. It is shown that the static susceptibility cannot diverge within the single site CPA. Characterizing the phase transition by the softening of the lowest mode in the spectrum. The stability conditions for the polarized phase at T=O are then determined.