Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model (original) (raw)

On the Phase Structure of the 3D Edwards Anderson Spin Glass

1998

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses. Recent numerical simulations [1, 2] have given a strong numerical evidence of the existence of a spin glass phase transition in the 3D Edwards Anderson spin glass (for a critical point of view see [3, 4, 5]). The first studies of such models are today 15 years old (for a recent review see [6]), and the Replica Symmetry Breaking (RSB) mean field solution [7] is found

Phase structure of the three-dimensional Edwards-Anderson spin glass

Physical Review B, 1998

Lack of Ultrametricity in the Low-Temperature Phase of Three-Dimensional Ising Spin Glasses

Physical Review Letters, 2004

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short-range Ising spin-glass (3DISG). By using clustering to focus on the relevant parts of phase space and reduce finite size effects, we found that for the SK model ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e., lack of ultrametricity. Another method, which does not rely on clustering, indicates that the mean-field solution works for the SK model but does not apply in detail to the 3DISG, for which stochastic stability is also violated.

Numerical study of the two-replica overlap of the 3D Edwards–Anderson Ising spin glass

Physica A: Statistical Mechanics and its Applications, 2003

We present results of recent high-statistics Monte Carlo simulations of the Edwards-Anderson Ising spin-glass model in three dimensions. The study is based on a non-Boltzmann sampling technique, the multi-self-overlap algorithm which is specifically tailored for sampling rare-event states. We thus concentrate on those properties which are difficult to obtain with standard canonical Boltzmann sampling such as the free-energy barriers F q B in the probability densities P J (q) of the Parisi overlap parameter q and the behavior of the tails of the disorder averaged density P (q) = [P J (q)] av. Our results for the tails disagree with mean-field predictions and support extreme order statistics over many orders of magnitude.

Multioverlap Simulations of the 3D Edwards-Anderson Ising Spin Glass

Physical Review Letters, 1998

We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter q is achieved. Canonical expectation values for the entire q-range (multi-overlap) follow by re-weighting. We demonstrate the feasibility of the approach by studying the 3d Edwards-Anderson Ising (J ik = ±1) spin glass in the broken phase (β = 1). For the first time it becomes possible to obtain reliable results about spin glass tunneling barriers. In addition, as do some earlier numerical studies, our results support that Parisi mean field theory is valid down to 3d.

Static versus Dynamic Heterogeneities in the D=3 Edwards-Anderson-Ising Spin Glass

Physical Review Letters, 2010

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey Finite-Size Scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a Finite-Time Scaling Ansatz, with potential implications for experimental work. PACS numbers: 75.50.Lk, 75.40.Mg, 75.10.Nr Spin glasses, fragile molecular glasses, polymers, colloids, and many other materials display a dramatic increase of characteristic times when cooled down to their glass temperature, T g [1]. This is probably due to the collective movements of an increasing number of elements in the system, with a (free) energy barrier growing with the size of the cooperative regions [2] (the cooperative regions become larger as the temperature gets closer to T g ). Experimentally, one can get the fingerprints of these movements by observing dynamical heterogeneities [3] or non-linear susceptibilities .

Frustration and ground-state degeneracy in spin glasses

Physical Review B, 1977

The problem of an Ising model with random nearest-neighbor interactions is reformulated to make manifest Toulouse's recent suggestion that a broken "lattice gauge symmetry" is responsible for the unusual properties of spin glasses. Exact upper and lower bounds on the ground-state energy for models in which the interactions are of constant magnitude but fluctuating sign are obtained, and used to place restrictions on possible geometries of the unsatisfied interactions which must be present in the ground state. Proposed analogies between the ferromagnetspin-glass phase boundary at zero temperature and a percolation threshold for the "strings" of unsatisfied bonds are reviewed in the light of this analysis. Monte Carlo simulations show that the upper bound resulting from a "one-dimensional approximation" to the spin-glass ground-state energy is reasonably close to the actual result. The transition between spin glass and ferromagnet at 0 K appears to be weakly first order in these models. The entropy of the ground state is obtained from the temperature dependence of the internal energy, and compared with the density of free spins at very low temperatures. For a two-dimensional spin glass in which half the bonds are antiferromagnetic, S(0)-0.099 k~; for the analogous three-dimensional spin glass the result is S(0)-0.062 k~. Monte Carlo kinetic simulations are reported which demonstrate the existence and stability of a fieldcooled moment in the spin-glass ground state.

Low-temperature phase boundary of dilute-lattice spin glasses

2008

The thermal-to-percolative crossover exponent , well known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p c using an improved reduction algorithm. Simulations extend to system sizes above N =10 8 in dimensions d = 2 ,. .. , 7. The results can be related to the behavior of the transition temperature T g ϳ͑p − p c ͒ between the paramagnetic and the glassy regime for p p c. In three dimensions, where our simulations predict = 1.127͑5͒, this scaling form for T g provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimensions near and above the upper critical dimension, the results provide a challenge to reconcile mean-field theory with finite-dimensional properties.

A numerical investigation of the overlap distribution among pure states in the spin glass phase

1984

Abstract We use zero temperature mean field equations to study numerically several properties of the Sherrington-Kirkpatrick model. In particular we observe the fluctuations from sample to sample of the order parameter q (x) and see partial evidence of the ultrametricity structure among pure states. Résumé A partir des équations de champ moyen à température nulle on étudie numériquement les propriétés du modèle de Sherrington-Kirkpatrick.

Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model (original) (raw)

Related papers