Van Hemmen Model Research Articles

The Anisotropic van Hemmen model with a random field in a random network

In this paper we investigate the three-state spins van Hemmen model with a crystalline field in the random network. The van Hemmen model is known for being treated without the use of replicas. The same method used by van Hemmen is utilized here to average over disordered exchange interactions. To deal with averages over the realizations of the lattice we utilized the replica symmetry formalism of order parameter functions. The order parameters calculated to detect which phase the system encounters are calculated numerically by means of a population dynamics algorithm. Firstly we obtained phase diagrams in low fixed temperature in the diagram crystalline field versus random field, we observe higher connectivities to give rise to segregation between high activity and low activity spin glass (SG) phases, also we verify the appearance of a tricritical point in the low crystalline field region. Finally to account the effects of high thermal fluctuations we have drawn phase diagrams in the temperature versus random field plane for fixed values of crystalline field. Here we observe an important modification of the phase plane topology by the increment of network connectivity. It is also notable the presence of a reentrant behavior in first and second order phase transitions when the crystalline field is sufficiently large.

Unfolding of phases and multicritical points in the classical anisotropic van Hemmen spin glass model with random field

We study magnetic properties of the 3-state spin ($S_{i}=0$ and $\pm 1$) spin glass (SG) van Hemmen model with ferromagnetic interaction $J_0$ under a random field (RF). The RF follows a bimodal distribution The combined effect of the crystal field $D$ and the special type of on-site random interaction of the van Hemmen model engenders the unfolding of the SG phases for strong enough RF, i. e., instead of one SG phase, we found two SG phases. Moreover, as $J_0$ is finite, there is also the unfolding of the mixed phase (with the SG order parameter and the spontaneous magnetization simultaneously finite) in four distinct phases. The emergence of these new phases separated by first and second order line transitions produces a multiplication of triple and multicritical points.

The van Hemmen model and effect of random crystalline anisotropy field

In this work, we have presented the generalized phase diagrams of the van Hemmen model for spin S=1 in the presence of an anisotropic term of random crystalline field. In order to study the critical behavior of the phase transitions, we employed a mean-field Curie–Weiss approach, which allows calculation of the free energy and the equations of state of the model. The phase diagrams obtained here displayed tricritical behavior, with second-order phase transition lines separated from the first-order phase transition lines by a tricritical point.

Weak randomness in geometrically frustrated systems: spin-glasses

We study the competition between the spin-glass (SG) phase and antiferromagnetic (AF), superantiferromagnetic or ferromagnetic (FE) order in geometrically frustrated systems. We consider a model with two types of frustration: one coming from disordered interactions (J) and another coming from the square-lattice Ising spin system with first-(J1) and second-(J2) neighbor interactions (intrinsic frustration). The disordered interactions are between clusters and they follow the van Hemmen model, which represents a limit of weak frustration. The cluster mean-field approximation is used to treat the short-range intercluster interactions. Results are exhibited in phase diagrams of the temperature T versus J for several values of . When the intrinsic frustration increases, the Néel and Curie temperatures decrease at the same time so that the SG phase appears at a lower J. Moreover, the FE correlations enhance the SG behavior, while AF correlations reduce the SG region at the same level of intrinsic frustration. These results indicate that a weak disorder in geometrically frustrated systems is able to stabilize the SG phase.

The van Hemmen–Kondo model for disordered cerium systems

The interplay between disorder and strong correlations has been observedexperimentally in disordered cerium alloys such as Ce(Ni, Cu) orCe(Pd, Rh). In the case of Ce(Ni, Cu) alloys with a Cu concentrationx between 0.6 and 0.3, the first studies have shown a smooth transition withdecreasing temperature from a spin glass phase to ferromagnetism; forx smaller than 0.2, a Kondo phase has been observed. The situation is more complicated nowdue to the recent observation of magnetic clusters. The competition between the Kondo effect,the spin glass (SG) and the ferromagnetic (FE) ordering has been extensively studiedtheoretically. The Kondo effect is described by the usual mean-field approximation; we havetreated the SG behavior successively by the Sherrington–Kirkpatrick model, then by theMattis model and finally by the van Hemmen model, which takes both a ferromagnetic partand a site-disorder random part for the intersite exchange interaction. We present here theresults obtained by the van Hemmen–Kondo model: for a large Kondo exchangeJK, a Kondo phase is obtained while, for smallerJK, the succession of an SG phase, a mixed SG–FE one and finally an FE one has beenobtained with decreasing temperature. This model improves the theoretical description ofdisordered Kondo systems by providing a simpler approach for further calculations ofmagnetic clusters and can, therefore, account for recent experimental data on disorderedcerium systems.

Fermionic van Hemmen spin glass model with a transverse field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field Γ. 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 Γ. 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 μ and Γ. The Γ field suppresses the magnetic orders. The increase of μ 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 μ. In addition, μ can change the nature of the phase boundaries introducing a first order transition.

Van Hemmen-Kondo model for disordered strongly correlated electron systems

We present here a theoretical model in order to describe the competition between the Kondo effect and the spin glass behavior. The spin glass part of the starting Hamiltonian contains Ising spins with an intersite exchange interaction given by the local van Hemmen model, while the Kondo effect is described as usual by the intrasite exchange ${J}_{K}$. We obtain, for large ${J}_{K}$ values, a Kondo phase and, for smaller ${J}_{K}$ values, a succession, with decreasing temperature, of a spin glass phase, a mixed spin glass-ferromagnetic one and finally a ferromagnetic phase. This model improves the theoretical description of disordered Kondo systems with respect to previous models and can account for experimental data in Cerium disordered systems such as ${\text{CeCu}}_{1\ensuremath{-}x}{\text{Ni}}_{x}$ alloys.

The random cluster approach in the Kondo Lattice model

We present here a Kondo Lattice model with an intersite random coupling between localized magnetic moments, which is composed of two terms, a random one given by the van Hemmen model and a ferromagnetic one. This model can be used to study new experimental evidences indicating the existence of a complex magnetic arrangement in CeNi1−xCux alloys showing, with decreasing temperature, a glassy Kondo behavior and then a disordered ferromagnetism. We treat here the randomness without the replica method and found a phase which describes some features of the spin glass approach within the van Hemmen model. This approach, which takes both Kondo and ferromagnetic interactions, is suitable to describe correctly the phase diagram of CeNi1−xCux alloys, with in particular the existence of the mixed spin glass-ferromagnetic at very low temperatures.

The van Hemmen model in the presence of a random field

The van Hemmen model with a random field is studied to analyze the tricritical behavior in the Ising spin glass phase. The free energy and phase diagram (T versus H and T versus Jo/J, where H is the root mean square deviation of the magnetic field, Jo and J are the ferromagnetic and root mean square deviation exchange, respectively) are calculated for the model with discrete (or bimodal) and Gaussian distributions. For the case of the bimodal probability distribution (random field and exchange), we have the presence of three ordered phases, namely: spin glass (SG), mixed (pi) and ferromagnetic (F). The root mean square deviation of the random field H destroys the spin glass and mixed phases. The mixed phase doesn't appear with Gaussian distribution. In the plane T versus H, we analyze the tricritical behavior for the case of the bimodal distribution, and we compare it with the results obtained by using the Gaussian distribution that presents only second-order phase transition.

First-order phase transition in the quantum spin glass at T=0

The van Hemmen model with transverse and random longitudinal field is studied to analyze the tricritical behavior in the quantum Ising spin glass at T=0. The free energy and order parameter are calculated for two types of probability distributions: Gaussian and bimodal. We obtain the phase diagram in the Ω– H plane, where Ω and H are the transverse and random longitudinal fields, respectively. For the case of Gaussian distribution the phase transition is of second order, while the bimodal distribution we observe second-order transition for high-transverse field and first-order transition for small transverse field, with a tricritical point in the phase diagram.

Dynamical phase diagram of the van Hemmen model of spin glass

The dynamical behaviour of the van Hemmen model of spin glass is studied by comparing the time evolution of two configurations subjected to the same thermal noise. It was found that the system undergoes several dynamical phase transitions among the paramagnetic, ferromagnetic, spin-glass and mixed phases, The dynamical phase diagram seems to be in good agreement with the static one. In the spin glass phase, the system presents a quite different dynamical behaviour from that found in short-range spin glass models as well as in the Sherrington-Kirkpatrick model.

Reentrant transitions in the van Hemmen model of a spin glass

The van Hemmen model of a spin glass, which is an Ising model with random couplings J ij between sites i and j equal to J 0 + J(ξ i η j + ξ j η i ), where (ξ i , η i ) are independent, identically distributed random variables, is studied in the pair approximation of the cluster variation method. For the family of probability distributions 1 2 (1 − p)δ(ξ i − a) + pδ(ξ i ) + 1 2 (1 − p)δ(ξ i + a), where p is varied, phase diagrams are constructed. They are qualitatively different from the mean-field phase diagrams and display a competition between tendencies towards spin-glass and towards ferromagnetic ordering, which results in reentrant transitions. It is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system.

The short-range van Hemmen model in a simple Kikuchi approximation: Comparison with the mean-field model and with spin-glasses

Abstract A simple first-order Kikuchi approximation is studied for the short-range (nearest-neighbour) version of the van Hemmen mean-field model originally proposed for spin-glasses. Although the approximation is very similar to the mean-field treatment, the phase diagrams from the two methods are drastically different. Previously reported results are reviewed and extended. The “reentrant” ferromagnetic to “spin-glass” transition found in zero magnetic field persists in small fields. The equilibrium magnetization displays a maximum as a function of temperature in the reentrance region. The characteristic S-shape of the magnetization versus field in the “spin-glass” region and magnetic hysteresis are observed. In addition, some exact results concerning the problem of the lower critical dimension of the short-range model are derived.