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.     

Dynamics of a soft-spin van Hemmen model. I. Phase and bifurcation diagrams for stationary distributions

The dynamics of a soft-spin version of the van Hemmen spin-glass model is considered in the thermodynamic limit. Phase and bifurcation diagrams for quenched distributions are given. Phase coexistence, metastability, and hysteretic phenomena are found.     

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.     

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 J₀ + J(ξ_iη_j + ξ_jη_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 − p)δ(ξ_i − a) + pδ(ξ_i) + (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.     

Fluctuation-dissipation ratio in three-dimensional spin glasses

We present an analysis of the data on aging in the three-dimensional Edwards-Anderson spin-glass model with nearest-neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean-field theory. We measure the parameterx(q) describing the violation of the relation among correlation and response functions implied by the fluctuation-dissipation theorem.     

Multicanonical recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.     

Dynamical renormalization of kinetic van der Waals spin models

An exact dynamical renormalization approach in differential form is proposed for kinetic van der Waals spin systems with general many-body interactions. The problem of restoring covariance in the evolution equation after renormalization of the model is solved by introducing a suitable renormalized time parameter, which depends also on the magnetization of the spin configuration. The study of the behavior of this renormalized time near criticality leads to a scaling relation for the linear relaxation time. This relation can be shown to imply the exact results for the dynamical critical behavior of the system.On leave of absence from Instituto di Fisica e Unità G.N.S.M. del C.N.R., Università di Padova, Padova, Italy.     

A mixed phase transition for a hierarchical spin glass

A proof of the existence of a mixed ferromagnetic (or antiferromagnetic)-spin-glass fixed point for an Ising spin-glass model on the diamond hierarchical lattice is given.     

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.     

Differential renormalization of van der Waals spin models

An exact renormalization group equation in differential form is derived for spin systems with general many-body interactions in the van der Waals limit. This equation is solved and the free energy is determined as an integral along the renormalization trajectory in the interaction space. It is shown that the transformation can always be modified in such a way that an undetermined integration constant for the free energy vanishes exactly, also below the critical temperature. We also demonstrate how the invariance of the free energy under a parameterdependent equivalence transformation can provide information about the critical behavior of the system. In this alternative approach dangerous irrelevant variables play an essential role.On leave of absence from Istituto di Fisica e Unità GNSM del CNR, Università di Padova, Padova, Italy.     

Generic spiral spin liquids

Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally fluctuate cooperatively from a collection of spiral configurations at low temperatures. These spiral propagation wavevectors form a continuous manifold in reciprocal space, i.e., a spiral contour or a spiral surface, that strongly governs the low-temperature thermal fluctuations and magnetic physics. In this paper, the relevant spin models conveying the spiral spin liquid physics are systematically explored and the geometric origin of the spiral manifold is clarified in the model construction. The spiral spin liquids based on the dimension and the codimension of the spiral manifold are further clarified. For each class, the physical properties are studied both generally and for specific examples. The results are relevant to a wide range of frustrated magnets. A survey of materials is given and future experiments are suggested.     

Spin frustration-related behavior of mixed spin diamond chain

The magnetization of mixed spin-1/2, 1 Ising diamond chain with antiferromagnetic spin exchange interaction has been investigated by using the Monte Carlo simulation. Magnetization behaviors with different antiferromagnetic interactions are simulated under magnetic field at low temperature. The behaviors are studied in two different cases. In one case the absolute value of the interaction between two spin-1/2 atoms is the largest and in the other case it is not the largest. Multiple plateaus of magnetization M, such as plateaus at M=±1, M=0 and M=±0.566 are obtained. The plateaus at M=±0.566 correspond to two metastable states. The M=0 plateau may disappear at some specific values of spin exchange interactions. The spin configurations were checked when the plateaus appear. The dimmer and trimmer states are found.     

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.     

1/f noise and resistivity of spin glasses

Electrical resistivityρ(T) of spin glasses within the framework of Mookerjee and Chowdhury’s percolation model where there is a distribution of relaxation times (drt) is calculated.ρ(T) thus calculated is in better qualitative agreement with experimental results than that in the single relaxation time model.     

感染生长模型的逾渗模拟

在规则格子点阵中，活跃点逐步动态地以可变概率感染附近空缺点而生成系综.利用感染概率替代系综温度，给粒子划分能级，可以用巨正则系综配分函数表征体系.蒙特卡洛方法模拟验证了该体系在逾渗阈值处的相变行为.提出了一种新的较为普适的估算规则点阵逾渗阈值的方法.对介质基底上金属薄膜的实验研究验证了该感染生长模型的合理性.由此给出了格子点阵的固有属性(逾渗)如何在粒子聚集成团簇这一动态过程中体现出来的物理模型. 关键词： 逾渗 系综 蒙特卡洛方法 生长模型     

Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field

We study the four dimensional (4D) ±J Ising spin glass in a magnetic field with the simulated tempering algorithm recently introduced by Marinari and Parisi. We compute numerically the order parameter function P(q) and analyze the temperature dependence of the first four cumulants of the distribution. We discuss the evidence in favor of the existence of a phase transition in a field. Assuming a well defined transition we are able to bound its critical temperature.     

The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization. Received 27 September 2000     

The traveling salesman problem and its analogy with two-dimensional spin glasses

The low-temperature regime of the Euclidean traveling salesman problem is studied numerically. The specific heat behavior is analyzed in terms of the number of cities and compared with that of spin-glasses. A properly defined order parameter shows the existence of freezing effects at low temperature. The Euclidean TSP behaves as a spin glass in two dimensions.     

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.