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.     

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

The inverse freezing (IF) is studied with a quantum fermionic van Hemmen spin glass (SG) model. The disorder is treated without the use of replica method, in which an exact mean field solution is obtained for two different types of quenched disorders: the bimodal and the gaussian ones. The IF is then observed for certain range of chemical potential when the gaussian distribution is adopted. However, IF is destroyed by the quantum fluctuations. Particularly, the results suggest that the nontrivial SG free energy landscape, represented by strong disordered SG models, is not a necessary condition to generate a spontaneous IF.     

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.     

Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop

The Ising spin glass model on Bethe-like lattices (cactus lattices) is studied using replicas in the presence of a magnetic field. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained close to the spin glass transition temperature. The results are compared with those for the Bethe lattice to see the effects of loops. The slope of the order parameter function diminishes considerably for both lattices compared with that for the Sherrington–Kirkpatrick (SK) model. The loci of the AT line for the cactus lattices and the Bethe lattice are above and below that for the SK model, respectively.     

Replica symmetry breaking for the Ising spin glass within cluster approximations

Within a class of cluster approximations, the Ising spin glass model on a d-dimensional hypercubic lattice is solved near the spin glass transition temperature. Spin glass order parameter function and Almeida-Thouless line are obtained.     

Local field distribution revisited in the light of percolation model of spin glass transition

The existence of a ‘hole’ in the local field distributionP(H) in canonical spin glasses is proved in the framework of Mookerjee and Chowdhury’s percolation model of spin glass transition.     

Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields

The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.     

Replica symmetric spin glass field theory

A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v)$g(v)$. Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v)$g(v)$ can be derived, whereas it can be exactly computed in the mean field Sherrington–Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d?6$d?6$, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.     

Sherrington-Kirkpatric自旋玻璃模型的非平衡态性质

通过动力学蒙特卡罗模拟对Sherrington-Kirkpatric （SK）自旋玻璃模型进行研究. 结果表明,弱场下自旋玻璃的磁化率在转变点非常陡峭,而比热容则呈现比较宽的转变. 同时,也成功地模拟了自旋玻璃体的年龄效应和记忆效应. 通过模拟发现,不同的弛豫时间对系统的能量影响很大,这直接导致了年龄效应和记忆效应;各向同性的SK模型不能给出实验中的交换偏移现象. 关键词： 自旋玻璃 记忆效应 年龄效应 磁化率     

Infinite range Ising spin glass model with a transverse field

The infinite range Ising spin glass model with a transverse field is studied by the pair approximation extended to include quantum effects. A mean field equation is obtained and the transition temperature T_c is shown to increase linearly with the transverse field Γ when Γ is small.     

Cluster spin glass in concentrated alloys

Spin glass and structural states of Ni-Mn, Ni₃Mn-Ni₃V and Ni₃Mn-Ni₂Cr systems of alloys are investigated. The “freezing” temperature T _g of spin glass and Curie temperatures are obtained from the temperature dependence of the differential magnetic susceptibility χ_ac. Structural states of alloys are studied by the neutron diffraction technique. A cluster mechanism of spin glass formation is established.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Finite-dimensional spin glass and quantum error correcting code

We study a variety of spin systems with randomness in order to investigate the performance of the quantum error correcting codes. We show that the duality formalism is useful to search the locations of the critical points for the random spin systems, which gives us the clue to the exact values of the accuracy thresholds for the topological error correcting codes.     

Convergence to the ground-state energy in the thermodynamic limit of the Ising model in a strong transverse field

For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the diameter of thed-dimensional lattice is given byL, the absolute value of the difference of the ground-state energy per site and its limit is asymptotically exp(-L)L ^–d/2 for some positive constant. We also show that the correlation function has the same behavior. Our results are derived by cluster expansions, using a method of Bricmont and Fröhlich which we extend to the quantum mechanical case.     

The magnetic field effects on the frustrated antiferromagnetic spin chain

We presented a numerical study of the magnetization process of frustrated spin-1/2 chain. Using the exact diagonalization technique, we provided the evidence that a plateau at one-third of the saturation magnetization exists in the magnetization curve of frustrated antiferromagnetic spin-1/2 chain.     

Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass

Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.