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.
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.
A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,T plane is also given.
Anisotropic dipolar systems are considered. Such systems in an external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions, this model yields a spin glass to paramagnet phase transition as a function of the transverse field. We show that the off-diagonal dipolar interaction, although effectively reduced, induces a finite correlation length and thus destroys the spin-glass order at any finite transverse field. We thus explain the behavior of the nonlinear susceptibility in the experiments on LiHo(x)Y(1-x)F(4), and argue that a crossover to the paramagnetic phase, and not quantum criticality, is observed.
We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.
We examine the quantum phase transition at zero temperature between paramagnetic and spin-glass-ordered phases as the strength of a uniform transverse field, \ensuremath{\Gamma}, is varied. At the critical point, ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$, the spin autocorrelation function decays with time, t, as ${\mathit{t}}^{\mathrm{\ensuremath{-}}2}$. As the transition is approached from the paramagnetic phase the nonlinear susceptibility diverges as {\ensuremath{\Vert}ln(\ensuremath{\Gamma}-${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$)\ensuremath{\Vert}/(\ensuremath{\Gamma}-${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$)${\mathrm{}}}^{1/2}$.
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.
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field Γ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of Γ and for system sizes N≤16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of Γ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γc≃1.5. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get z=2.1±0.1 which is in contradiction with a recent estimate (z=4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ<Γc.