Quantum Ising spin-glass

Geoffrey Grimmett

Raimundo R. dos Santos, Rita Zorzenon dos Santos, Mauricio Kischinhevsky

We discuss the zero-temperature behavior of the transverse Ising spin-glass ($\ifmmode\pm\else\textpm\fi{}{J}_{0}$) model. The $d$-dimensional quantum model is shown to be equivalent to a classical ($d+1$)-dimensional Ising spin glass with correlated disorder. A renormalization-group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin glass in two dimensions.

Geoffrey Grimmett

Bikas K. Chakrabarti

In view of the indications of nontrivial quantum effects on the spin-glass ground-state (frustration, etc.) properties, the Ising spin-glass models (both frustrated and unfrustrated) are investigated here in the presence of a transverse field to study the possible quantum effect on the corresponding (classical) Ising spin-glass behavior. Studies on the critical behavior show similar quantum effects as observed in other established second-order transitions.

C.V. Morais

The present work studies inverse transitions by using two spin glass models: the infinite-range fermionic Ising spin glass (FISG) in the presence of a transverse magnetic field ¡ and Hopfield fermionic Ising spin glass (HFISG) model with a ¡ field. In these models, the spin are written in terms of fermionic operators. In that case, there are four possible eigenvalues of the operator Sz i , two of them non-magnetic. The problem for both models is expressed in the path integral formalism with Grassmann variables. Particularly, the FISG and HFISG models are analysed in the Grand Canonical ensemble, which allows changing the average number occupation of fermions per site by adjusting the chemical potential μ, which is a magnetic dilution mechanism. The Grand Canonical Potential is obtained within the static approximation with replica symmetry and one-step replica symmetry breaking schemes. Firstly, the highly frustrated FISG model is studied. Essentially, for ¡ = 0, a first order inverse transition arises with the increase of μ (dilution). As a consequence, the inverse transitions can be studied under the effect of quantum fluctuations when a transverse magnetic field ¡ is turned on. As main result, it is shown that quantum fluctuations destroy the inverse transitions. Secondly, the role of frustration as ingredient for a model to present naturally inverse transitions is checked by the HFISG model, which allows interpolating from trivial randomness to a highly frustrated regime. In fact, it is shown that for ¡ = 0 and high values of μ, any frustration level presents a inverse transition. Finally, the introduction of the ¡ field in the HFISG model allows to study how the simultaneous adjusting of quantum fluctuations and the level of frustration affects the inverse transition in this model. As a result, it is suggested that the interplay between the dilution and the presence of a frustrated phase has an important role inverse transitions producing. In addition, when the effects of quantum fluctuations are introduced by ¡, the role of dilution seems to be weakened. As a consequence, the inverse transition is destroyed in HFISG model.

Subir Sachdev A