We propose a method to study the magnetic properties of a disordered Ising kagome lattice. The model considers small spin clusters with infinite-range disordered couplings and short-range ferromagnetic (FE) or antiferromagnetic interactions. The corr
elated cluster mean-field theory is used to obtain an effective single-cluster problem. A finite disorder intensity in FE kagome lattice introduces a cluster spin-glass (CSG) phase. Nevertheless, an infinitesimal disorder stabilizes the CSG behavior in the geometrically frustrated kagome system. Entropy, magnetic susceptibility and spin-spin correlation are used to describe the interplay between disorder and geometric frustration (GF). We find that GF plays an important role in the low-disorder CSG phase. However, the increase of disorder can rule out the effect of GF.
The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provi
des a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.
The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from GS model without RF suggest that disorder and frustration are the key ingredients to produce spontaneous invers
e freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field $D$, is gradually suppressed when the RF is increased.
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 analys
is 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.
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.
The physics of disordered alloys, such as typically the well known case of CeNi1-xCux alloys, showing an interplay among the Kondo effect, the spin glass state and a magnetic order, has been studied firstly within an average description like in the S
herrington-Kirkpatrick model. Recently, a theoretical model (PRB 74, 014427 (2006)) involving a more local description of the intersite interaction has been proposed to describe the phase diagram of CeNi1-xCux. This alloy is an example of the complex interplay between Kondo effect and frustration in which there is in particular the onset of a cluster-glass state. Although the model given in Ref. PRB 74, 014427 (2006) has reproduced the different phases relatively well, it is not able to describe the cluster-glass state. We study here the competition between the Kondo effect and a cluster glass phase within a Kondo Lattice model with an inter-cluster random Gaussian interaction. The inter-cluster term is treated within the cluster mean-field theory for spin glasses, while, inside the cluster, an exact diagonalisation is performed including inter-site ferromagnetic and intra-site Kondo interactions. The cluster glass order parameters and the Kondo correlation function are obtained for different values of the cluster size, the intra-cluster ferromagnetic coupling and the Kondo intra-site coupling. We obtain, for instance, that the increase of the Kondo coupling tends to destroy the cluster glass phase.
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 obt
ain 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.
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.
