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physica status solidi (b)

On the Theory of the Ising Model with a Transverse Field

G. Kamieniarz

Published Jun 1, 1978• 1 citation
Publisher

Abstract

Abstract The zero‐temperature behaviour of the transverse Ising model is investigated in the paramagnetic region. Two versions of the Green's function technique are used and the results are in excellent agreement with the high density and series expansions results in both, the weak and strong interaction limit.
DOI
10.1002/pssb.2220870206

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Physical Review Letters•Aug 17, 1970•143 citations
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.
Both weak-coupling and strong-coupling series expansions are calculated for the Ising model in a transverse field at zero temperature in three dimensions. Series are obtained for the ground-state energy, the magnetization, the susceptibility, and the energy gaps, on the simple cubic, the body-centred cubic and the face-centred cubic lattices. The analysis of the critical behaviour is consistent with the behaviour predicted by renormalization group theory for the four-dimensional simple Ising model. There is a remarkable degree of universality between all three lattices.
Abstract The Ising model in a transverse field is treated by means of Green function technique to calculate the dynamic structure factor above and below Tc. The soft mode is overdamped in the disordered phase and near Tc, while it is nearly undamped at low temperatures. The coupling between the transverse soft mode and the relaxing longitudinal mode produces a central mode in the dynamic structure factor. The temperature dependence of the dynamic structure factor for zero wave vector is calculated numerically.
The phase transition in the Ising model has been studied as a function of an applied transverse field, by Green's function and series-expansion methods. The critical indices are probably independent of the applied field except at T=0T=0T=0 where they appear to be related to those of the Ising model in one higher dimension.