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physica status solidi (b)

Central Peak in Ising Model with Transverse Field (II)

V. N. Kashcheev

Published Jul 1, 1983• 0 citations
Publisher

Abstract

Abstract It is shown that in the hydrodynamic limit the central peak, traced back to the interaction of the pseudospin critical fluctuations with thermal diffusion mode in the Ising model with a transverse field, has the Lorentz form. The critical exponent of the width of this peak is calculated.
DOI
10.1002/pssb.2221180150

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Journal of Physics C Solid State Physics•Oct 28, 1971•214 citations
Dynamics and the approximate thermodynamical properties of the classical Ising model in a transverse field (CIMTF) are studied. This is done by elucidating a close correspondence of the CIMTF to a nonlinear lattice field in which each atom, while coupled harmonically with its neighbours, sits on on-site anharmonic potential. It is shown that when the ratio of the Ising interaction to a transverse field-strength exceeds a certain critical value, the on-site potential is of double-well type with saturable nonlinearity. Domain wall modes and magnon modes in continuous one-dimensional CIMTF are studied for both systems to substantiate the correspondence. By exploiting this, a brief study is made on the approximate properties of the free energy and of the dynamical structure factor S ( k ,ω) of longitudinal spin fluctuations of the CIMTF. These quantities are shown to be composed of two contributions, one from domain-wall modes and the other from magnon modes, which manifest themselves as a central peak and side peaks in S ( k ,ω), respectively.
For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma i S i x - 1 / 2 Sigma i,j J ij S i z S j z , are studied by perturbation expansions at T=0 in the ground state, both below and above the critical field Gamma C , for an hypercubic lattice and short range interactions. The order parameter (S z ) and the correlation function G=) Sigma i S i z Sigma j S j z ) are calculated respectively below and above Gamma C . The gap in the excitation spectrum is also studied above the critical field. The critical behaviour obtained from these expansions at T=0 is different from that obtained at T finite and is shown to be analogous to the critical behaviour of the Ising model for a lattice with one more dimension.