The present work analyzes the fermionic Ising spin glass model in a transverse magnetic field. The problem is written in the Grand Canonical ensemble with the spin operators represented by bilinear combinations of fermionic fields. The transverse field is a spin "flip" mechanism and inserts quantum fluctuations, which can lead the transition temperature Tj to quantum critical point (QCP). In this case, the phase transition from spin glass to paramagnetic phases occurs in T = o. On the other hand, charge fluctuations controlled by chemical potentiall-L show the existence of a tricritical point. The replica method with replica symmetry and static approximation are used to solve this problem. However, the replica symmetry solution shows some problems, like negative entropy in low temperatures. Thus, the stability conditions are derived to test the generated solution of this IDodel. The main purpose of this work is to study the competition between spin glass and paramagnetic phases with both quantum and charge fluctuations. After the stability conditions are derived, a detailed sight into the generated solution is shown under the form of diagrams phase. The stability conditions, however, show another applications in the present problem, once they can be used, for instance, in the tricritical point derivation.
We show that fermion systems with random and frustrated interactions display a strong coupling between glassy order and fermionic correlations, which culminates in the implementation of Parisi replica permutation symmetry breaking (RPSB) in their zero-temperature quantum field theories. RPSB effects, setting in below fermionic de Almeida--Thouless (dAT) lines, become stronger as the temperature T decreases and play a crucial role for many physical properties within the entire low-
T regime. The Parisi ultrametric structure is shown to determine the dynamic behavior of fermionic correlations (Green's functions) for large times and for the corresponding low-energy excitation spectra, which is predicted to affect transport properties in metallic (and superconducting) spin glasses. Thus we reveal the existence and the detailed form of a number of quantum-dynamical fingerprints of the Parisi scheme. These effects, being strongest as $\stackrel{\ensuremath{\rightarrow}}{T}0,$ are contrasted with the replica-symmetric nature of the critical field theory of quantum spin glass transitions at
T=0, which display only small corrections at low T from RPSB. RPSB effects moreover appear to influence the loci of the ground state transitions at
O(T0) and hence the phase diagrams. From explicit solutions for arbitrary T we find a representation of the Green's function in the
T=0 limit. This leads to a map of the fermionic (insulating) spin glass solution to the local limit of a Hubbard model with random repulsive interaction. This map holds for any number of replica-symmetry-breaking steps K. We obtain the distribution of the Hubbard interaction U and its dependence on the order of RPSB. A generalized mapping between metallic spin glass and random U Hubbard model is conjectured. We also suggest that the new representation of the Green's function at
T=0 can be used for generalizations to superconductors with spin glass phases. Further generalizations due to Coulomb effects including a crossover from four-state per site to effectively three-state per site models in the $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ limit are briefly considered. We compare our spin glass results with recent $d=\ensuremath{\infty}$ (clean) Hubbard model analyses, paying particular attention to the common role of the corresponding Onsager reaction fields. We also present details of the phase diagrams, emphasizing the important role of the chemical potential $\ensuremath{\mu}.$ The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations and controlled by quantum statistics. A comparison with the diluted Sherrington-Kirkpatrick (SK) spin glass and with classical spin 1 models such as the Blume-Emery-Griffiths model is given. Our detailed analysis for the infinite-range model shows that spin glass order must decay discontinuously as $\ensuremath{\mu}$ exceeds a critical value, provided T is below the tricritical
Tc3 and that the
T=0 transition is of classical type. RPSB occurs in any case on the irreversible side of the (modified) dAT lines for the fermionic SK model and hence at least everywhere within a fermionic spin glass phase. Although the critical field theory of the quantum paramagnet to spin glass transition in metallic systems remains replica symmetric at
T=0, with only small corrections at low T from RPSB, the phase diagram is affected at
O(T0) by RPSB. Generalizing our results for the fermionic Ising spin glass we consider modifications in phase diagrams of models with spin and charge quantum dynamics such as metallic spin glasses.
The present work studies the counterintuitive phenomenon of inverse transitions (IT). The IT are a class of phase transitions (reversible) in which the ordered phase appears at higher temperatures than the disordered one. Different models have been proposed to describe characteristics of IT. The goal of this work is just to propose a model of disordered interactions, which is able to present general characteristics of a inverse transition type, the inverse freezing (IF). The IF is a reversible transition from a paramagnetic phase (PM) to the spin glass order (SG) on heating. Within this context the van Hemmen SG model is analyzed in a fermionic formulation, in which the spin operators are written as a bilinear combination of fermionic creation and annihilation operators. In this model the random interactions Ji j introduce disorder and frustration, and the chemical potential m controls the average occupancy of fermions per site. The problem is analyzed for two different types of quenched disorders: bimodal (discrete) and gaussian (continuous). It is important to note that the disorder in the model analyzed here were treated without the use of the replica method and its complications. The results depend on the particular disorder. The behavior of the order parameters, entropy and occupation number are analyzed. Phase diagrams of temperature T versus chemical potential m can then be build. A reentrance transition is found for a certain range of m when the gaussian distribution is adopted. This reentrance transition is associated with the IF that occurs in a first-order transition from the paramagnetic to the spin glass phase when the temperature increases. On the other hand, models following disordered interactions of Sherrington-Kirkpatrick (SK) type suggest that the onset of IF can be a consequence of complex scenario for the free energy. In these models the replica method is used to treat the disorder and the solutions present this complex scenario. However, from the results obtained in present fermionic van Hemmen model, it can be concluded that the necessary conditions for a model exhibit IF are the combined effects of frustration and magnetic dilution (favoring states not interacting, controlled by m). Thus, the treatment of model presented in this work does not use the replica method or the complicated scenario of free energy and it is able to reproduces the characteristics of an inverse freezing. This is attributed to the presence of frustration and magnetic dilution. Keywords: Disorder. Quantum Spin Glass. Fermionic model. Inverse transitions
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.
Models with range-free frustrated Ising spin interaction and additional Hubbard interaction are treated exactly by means of the discrete time slicing method of Grassmann-field theory. Critical and tricritical points, spin and charge correlations, and the fermion propagator are derived as a function of temperature and chemical potential $\ensuremath{\mu},$ of the Hubbard coupling U and the spin-glass energy J. U is allowed to be either repulsive
(U>0) or attractive
(U<0). Cuts through the multidimensional phase diagram are obtained. Analytical and numerical evaluations take important replica symmetry-breaking (RSB) effects into account. Results for the ordered phase are given at least in a one-step approximation (1RSB), and for
T=0 we report the first two-, three-, and four-step calculations (4RSB) for fermionic spin glasses. The use of exact relations and invariances under RSB together with 2RSB calculations for all fillings and 4RSB solutions for half filling allow to model exact solutions by interpolation. For
T=0, our numerical results provide strong evidence that the exact spin-glass pseudogap obeys $\ensuremath{\rho}{(E)=c}_{1}|E\ensuremath{-}{E}_{F}|$ for energies close to the Fermi level with ${c}_{1}\ensuremath{\approx}0.13.$ Rapid convergence of ${\ensuremath{\rho}}^{\ensuremath{'}}{(E}_{F})$ under increasing orders of RSB is observed and ${\ensuremath{\rho}}^{\ensuremath{''}}(E)$ is evaluated to estimate subleading powers. Over a wide range of the pseudogap and after a small transient regime $\ensuremath{\rho}(E)$ regains a linear shape with a larger slope and a small S-like perturbation. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of two-dimensional localized disordered fermionic systems. Beyond half filling we obtain a $\ensuremath{\nu}\ensuremath{-}1\ensuremath{\sim}(\ensuremath{\mu}\ensuremath{-}{U)}^{2},$ $\ensuremath{\mu}>~U$ dependence of the fermion filling factor $\ensuremath{\nu}.$ We find a half filling transition between a phase for $U>\ensuremath{\mu},$ where the Fermi level lies inside the Hubbard gap, into a phase where $\ensuremath{\mu}(>U)$ is located at the center of the upper spin-glass (SG) pseudogap (SG gap). For $\ensuremath{\mu}>U$ the Hubbard gap combines with the lower one of two SG gaps (phase I), while for $\ensuremath{\mu}<U$ it joins the sole SG gap which exists in this half-filling regime (phase II). Shoulders of the combined gaps are shaped by RSB due to spin-glass order. We predict scaling behavior at the half-filling transition which becomes continuous due to $\ensuremath{\infty}\mathrm{RSB}.$ Implications of the half-filling transition between the deeper insulating phase II and phase I for the eventual delocalization by additional hopping processes in itinerant model extensions are discussed. Possible metal-insulator transition scenarios are described. Generalizations to random Hubbard coupling and alloy models as well as frustrated magnetic interactions with ferro- or antiferromagnetic components are discussed.
We show that tricritical points displaying unusual behavior exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one-loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new
T=0 tricritical point of metallic quantum spin glasses are derived.