Low temperature nonequilibrium dynamics in transverse Ising spin glass

The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature T ₁ (lower than the spin glass transition temperature T _g ) the ac susceptibility decreases with time approximately in a logarithmic way as the system tends to the equilibrium. It is shown that the transverse field of tunneling has unessential effect on the nonequilibrium dynamical properties of the magnetic droplet system. The role of quantum fluctuations in the behavior of the ac susceptibility is discussed.Received: 26 February 2004, Published online: 18 June 2004PACS: 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.10.Nr Spin-glass and other random models - 75.50.Lk Spin glasses and other random magnets     

Cluster fermionic Ising spin glass model with a transverse field

The fermionic Ising spin glass (SG) model in the presence of a transverse magnetic field Γ is studied within a cluster mean field theory. The model considers an infinite-range interaction among magnetic moments of clusters with a short-range ferromagnetic intracluster coupling J₀. The spin operators are written as a bilinear combination of fermionic operators. In this quantum SG model, the intercluster disorder is treated by using a framework of one-step replica symmetry breaking (RSB) within the static approximation. The effective intracluster interaction is then computed by means of an exact diagonalization method. Results for several values of cluster size n_s, Γ and J₀ are presented. For instance, the specific heat can show a broad maximum at a temperature T^∗ above the freezing temperature T_f, which is characterized by the intercluster RSB. The difference between T^∗ and T_f is enhanced by Γ, which suggests that the quantum effects can increase the ratio T^∗/T_f. Phase diagrams (T versus Γ) show that the critical temperature T_f(Γ) decreases for any values of n_s and J₀ when Γ increases until it reaches a quantum critical point at some value of Γ_c.     

Inverse freezing in the Hopfield fermionic Ising spin glass with a transverse magnetic field

The Hopfield fermionic Ising spin glass (HFISG) model in the presence of a magnetic transverse field Γ is used to study the inverse freezing transition. The mean field solution of this model allows introducing a parameter a that controls the frustration level. Particularly, in the present fermionic formalism, the chemical potential μ and the Γ provide a magnetic dilution and quantum spin flip mechanism, respectively. Within the one step replica symmetry solution and the static approximation, the results show that the reentrant transition between the spin glass and the paramagnetic phases, which is related to the inverse freezing for a certain range of μ, is gradually suppressed when the level of frustration a is decreased. Nevertheless, the quantum fluctuations caused by Γ can destroy this inverse freezing for any value of a.     

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field Γ. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean J₀ and standard deviation J. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small g (g is the strength of the local superconductor coupling written in units of J), while the PAIR phase appears as unique solution for large g. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of Γ.     

Finite interaction range spin glass in the Ising model

Using the Ising model and the random-field approximation, it is demonstrated that, in amorphous diluted magnets and crystalline metal alloys, the nearest neighbor interaction promotes a superparamagnetic state, which is followed by “freezing” of the magnetic moments of clusters and by transition into a macrospin glass state (cluster spin glass) as the temperature decreases. A theoretical magnetic phase diagram is constructed.     

Partition function zeros and the three-dimensional Ising spin glass

We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×L_z, 4×4×L_z, and 5×5×L_z forL _z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.     

Hysteresis loops and susceptibility of a transverse Ising nanowire

In this work, the magnetization, susceptibility, and hysteresis loops of a magnetic nanowire are described by the transverse Ising model using the effective field theory within a probability distribution technique. The effects of the exchange interaction between core/shell and the external fields on the magnetization and the susceptibility of the system are examined. Some characteristic phenomena are found in the thermal variations, depending on the ratios of the physical parameters in the shell and the core.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

Critical thermodynamics of the two-dimensional +/-J Ising spin glass

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low lying excitations and by the way low energy domain walls proliferate in this model.     

A quadrangular transverse Ising nanowire with an antiferromagnetic spin configuration

The phase diagrams and the temperature dependences of magnetizations in a transverse Ising nanowire with an antiferromagnetic spin configuration are investigated by the use of the effective-field theory with correlations (EFT) and the core–shell concept. Many characteristic and unexpected behaviors are found for them, especially for thermal variation of total magnetization m_T. The reentrant phenomenon induced by a transverse field in the core, the appearance of a compensation point, the non-monotonic variation with a compensation point, the reentrant phenomena with a compensation point and the existence of both a broad maximum and a compensation point have been found in the thermal variations of m_T.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.