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.
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.
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.
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.
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.
In this work we study the effects of quantum fluctuations in a disordered magnetic system. We consider a cluster-spin Ising model with antiferromagnetic short range interactions (J0) and disordered long range interactions (J) between clusters, where the system is under the influence of a transverse magnetic field Γ. The analytic treatment of the model is done by the replica method and Trotter formalism, in which a cluster mean field, replica symmetric and static approximations are used. This allows us to obtain an effective model of a single cluster that is exactly diagonalized. Thermodynamic quantities like order parameter and free energy are obtained then, the phase diagrams are analyzed. They are shown in temperature versus J0=J phase diagrams for some intensities of Γ. With Γ = 0, when we decrease the temperature (for lower intensities of J0=J) a continuous phase transition between the paramagnetic and cluster spin glass state (CSG) is found. When we increase the ratio J0=J, the system presents the antiferromagnetic phase (AF). The CSG state and the AF phase are separated by first order transitions. In the intermediate region of disorder, there exist a small interval in the AF-PM transition that is first order. When Γ is increased, the transitions PM-AF and PM-VSC decrease toward critical points in the lower and higher disorder, respectively. It is worth to note, in the intermediate range of disorder, that the transition CSG-AF disappears, letting a PM phase between them, even for zero temperature. Besides that, the first-order region, in the PM-AF transition, turns into a second order phase transition, changing its criticality in the low temperature regime. Our results show that quantum fluctuations affects the phase transitions of the model being capable to suppress and/or change his criticality. The present work suggests a model and a mechanism of the change in the criticality away from the quantum critical point, helping the investigation of this interesting and recent topic.
In the present work, a fermionic infinite-range Ising spin glass (SG) model with a transverse field Γ is studied. The model is analyzed in a one-lattice structure (quantum SG) and in a two-sublattice structure (SG/antiferromagnetism (AF) competition). In these two cases, the exchange interactions are random variables that follow Gaussian probability distributions (SK interactions). For the two-sublattice model, spins of distinct sublattices can couple with an SK-type interaction with an AF average. For a general case of this model, the disordered interactions can also occur with spins of same sublattices. The problem is formulated in a Grassmann path integral formalism within the static ansatz. The replica method is applied to treat the disorder, in which the replica symmetry (RS) and one-step replica symmetry breaking (1P-RSB) approximations are used. The one-lattice model results provide evidences that the 1S-RSB can be used to improve the physical description of the ordered quantum SG phase treated by the replica method. In the two-sublattice model, a parallel magnetic field H breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase (SG+AF) characterizing an asymmetric RSB region. In this region, intra-sublattice disordered interactions V increase the difference between the RSB solutions of each sublattice. The freezing temperature (Tf ) shows a higher increase with H when V enhances. A discontinuous phase transition from the replica symmetry (RS) solution to the RSB solution can appear with the presence of an intra-sublattice ferromagnetic average coupling. The Γ field introduces a quantum spin flip mechanism that suppresses the magnetic orders leading them to quantum critical points. Results suggest that the quantum effects are not able to restore the RS solution. Therefore, the presence of both fields, Γ and H, produces effects that are in competition on Tf for instance. However, in the asymmetric RSB region, Γ can produce a stable RS solution at any finite temperature for a particular sublattice while the other sublattice still presents RSB solution for the special case in which only the intra-sublattice spins couple with disordered interactions.
We investigate the inverse freezing in the fermionic Ising spin-glass model in a transverse field $\ensuremath{\Gamma}$. 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 $\ensuremath{\Gamma}$. As a consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too.