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Register a new userRole of the transverse field in inverse freezing in the fermionic Ising spin-glass model
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We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field $Gamma$. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site $n$ is strongly affected by $Gamma$. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too.
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In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The Grand Canonical Potential is obtained within the static approximation and one-step replica symmetry breaking scheme. As a result, phase diagrams temperature {it versus} the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.
In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $Gamma$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by $Gamma$. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential $mu$ and $Gamma$. The $Gamma$ field suppresses the magnetic orders. The increase of $mu$ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by $mu$. In addition, $mu$ can change the nature of the phase boundaries introducing a first order transition.
The stability of spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field $Gamma$. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues $lambda_{pm}$ of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when $Gamma$ is increased. Therefore, this result suggests that the study of the replicon can not be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the $lambda_{pm}$ indicate instability problems for the SG solution close to all range of first order boundary.
The quantum critical behavior of the Ising glass in a magnetic field is investigated. We focus on the spin glass to paramagnet transition of the transverse degrees of freedom in the presence of finite longitudinal field. We use two complementary techniques, the Landau theory close to the T=0 transition and the exact diagonalization method for finite systems. This allows us to estimate the size of the critical region and characterize various crossover regimes. An unexpectedly small energy scale on the disordered side of the critical line is found, and its possible relevance to experiments on metallic glasses is briefly discussed.
We confirm the presence of a mean-field Bose glass in 2D quasicrystalline Bose-Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the Aubry-Andre model, where the lattice geometry is that of a square with a quasiperiodic onsite potential. Second, we consider the randomly disordered vertex model, which takes aperiodic tilings with non-crystalline rotational symmetries, and forms lattices from the vertices and lengths of the tiles. For the disordered vertex models, the mean-field Bose glass forms across large ranges of the chemical potential, and we observe no significant differences from the case of a square lattice with uniform random disorder. Small variations in the critical points in the presence of random disorder between quasicrystalline and crystalline lattice geometries can be accounted for by the varying coordination number and the different rotational symmetries present. In the 2D Aubry-Andre model, substantial differences are observed from the usual phase diagrams of crystalline disordered systems. We show that weak modulation lines can be predicted from the underlying potential and may stabilise or suppress the mean-field Bose glass in certain regimes. This results in a lobe-like structure for the mean-field Bose glass in the 2D Aubry-Andre model, which is significantly different from the case of random disorder. Together, the two quasicrystalline models studied in this work show that the mean-field Bose glass phase is present, as expected for 2D quasiperiodic models. However, a quasicrystalline geometry is not sufficient to result in differences from crystalline realisations of the Bose glass, whereas a quasiperiodic form of disorder can result in different physics, as we observe in the 2D Aubry-Andre model.
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