The van Hemmen Fermionic Ising Spin Glass (vH FISG) model in the presence of a transverse and a random magnetic field is adopted to study the inverse freezing (IF) transition, without using the replica method to treat the disorder. In this model, the spin interactions are given by a combination of random variables that follow Gaussian distribution. The random field (RF) also follows a Gaussian distribution. The introduction of allow us to investigate the IF under the effects of a disorder which is not a source of frustration. A particularity of this fermionic formalism is that the chemical potential and the provide a magnetic dilution and quantum spin flip mechanism, respectively. The results show a reentrant transition from the spin glass (SG) to the paramagnetic (PM) phase in the absence of and . This reentrance appears for a certain range of , in which is found a PM phase (at low temperatures) with lower entropy than the SG state, characterising the IF. However, the IF is gradually suppressed when the effects are intensified. In addition, the IF is completely destroyed by the quantum fluctuations provided by . Therefore, nontrivial disorder combined with dilution can bring a scenario favourable to the IF occurrence, while random fields and quantum fluctuations are against the IF.
The van Hemmen Fermionic Ising Spin Glass (vH FISG) model in the presence of a transverse and a random magnetic field is adopted to study the inverse freezing (IF) transition, without using the replica method to treat the disorder. In this model, the spin interactions are given by a combination of random variables that follow Gaussian distribution. The random field (RF) also follows a Gaussian distribution. The introduction of allow us to investigate the IF under the effects of a disorder which is not a source of frustration. A particularity of this fermionic formalism is that the chemical potential and the provide a magnetic dilution and quantum spin flip mechanism, respectively. The results show a reentrant transition from the spin glass (SG) to the paramagnetic (PM) phase in the absence of and . This reentrance appears for a certain range of , in which is found a PM phase (at low temperatures) with lower entropy than the SG state, characterising the IF. However, the IF is gradually suppressed when the effects are intensified. In addition, the IF is completely destroyed by the quantum fluctuations provided by . Therefore, nontrivial disorder combined with dilution can bring a scenario favourable to the IF occurrence, while random fields and quantum fluctuations are against the IF.
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.
This work analyzes a spin glass (SG) model with cluster in two versions: a classic version with Ising spins and in a fermionic version with spin operators. In this model, the basic entities are correlated clusters that interact each other disorderedly (intercluster interaction). It is also considered short-range interactions among spins belonging to the same cluster (intracluster interaction), which can be ferromagnetic (FE) or antiferro- magnetic (AF). Disordered intercluster interactions are analytically calculated by using the framework of Parisi one-step replica symmetry breaking. After this treatment, we get an effective single cluster model solved by exact diagonalization. The fermionic version of the model can introduce quantum fluctuations by means of a transverse magnetic field Γ. As a result, the linear susceptibility χ has a cusp at the transition temperature Tf and the specific heat Cv has a broad maximum at temperature T* about 20% above Tf . However, for Γ sufficiently high, this difference is greater. This behavior is observed by some authors for the compound LiHoxY1-xF4 at low concentration. Furthermore, the fermionic SG model with cluster in the grand canonical ensemble (where the chemical potential μ introduces charge fluctuations) is used to investigate the mechanisms responsible for the inverse freezing (IF). In this analysis, for a certain region of μ, a reentrance related to the inverse freezing arises. However, the increase of the FE intracluster interactions J0 can take the tricritical point to lower T, introducing a second-order IF transition. On the other hand, the Γ destroys gradually the inverse freezing. The necessary mechanisms for the emergence of inverse freezing transition are also studied using the cluster SG model in a classic version with Ising spins. This study is firstly conducted considering only firstneighbors intracluster interactions AF and in a second moment considering intracluster interactions among second neighbors, where it is possible to introduce intracluster geometrical frustration. The presence of antiferromagnetic intracluster interactions decreases the total magnetic moment of the clusters, leading to a PM phase with low entropy, favoring the appearance of inverse freezing. Moreover, the presence of geometrical frustration is contrary to the emergence of inverse freezing.
In this work we 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 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 inverse freezing (IF) transition is studied with a cluster fermionic Ising spin glass model in the presence of a transverse magnetic field Γ. The model considers a disordered infinite-range interaction among magnetic moments of the clusters with a short-range ferromagnetic intracluster coupling J 0 . The intercluster disorder is treated within a mean-field theory by using the framework of one-step replica symmetry breaking and the static approximation. This treatment results in an effective model that is computed by means of an exact diagonalization method. In particular, in this fermionic problem, the chemical potential μ and the Γ introduce cluster charge fluctuations and quantum spin flipping, respectively. The results indicate an IF transition for a certain range of μ. When the short-range interaction increases, the IF is still found. However, the intensity of J 0 can affect the charge fluctuation, introducing a second-order IF transition. On the other hand, the enhancement of Γ destroys the inverse freezing.
Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.