Critical behavior of three-dimensional Ising spin glass models (original) (raw)
Critical behavior of the three-dimensional Ising spin glass
Physical Review B, 2000
We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the nu\nunu and eta\etaeta critical exponents are also presented.
Critical parameters of the three-dimensional Ising spin glass
Physical Review B, 2013
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain T c = 1.1019 for the critical temperature, ν = 2.562(42) for the thermal exponent, η = −0.3900(36) for the anomalous dimension and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = −5.69(13), β = 0.782(10) and γ = 6.13(11). We also compute several universal quantities at T c .
Numerical evidence of a critical line in the 4d Ising spin glass
Europhysics Letters (epl), 1993
We study numerically the four-dimensional f J Ising spin-glass at nonzero external magnetic field, We find numerical evidence of the existence of the Almeida-Thouless critical line. The critical exponents differ from those found at zero external magnetic field.
Spin-s Spin-Glass Phases in the d=3 Ising Model
Physical Review E, 2021
All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s→∞. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of λ=1.93 and runaway exponent of yR=0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at pt=0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.
Short-range Ising spin glasses: a critical exponent study
Physica A: Statistical Mechanics and its Applications, 1998
The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension d f = 2.58, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent β is directly estimated from the data of the local Edwards-Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the ν exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space.
1997
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field Γ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of Γ and for system sizes N ≤ 16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of Γ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γ c ≃ 1.5. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get z = 2.1 ± 0.1 which is in contradiction with a recent estimate (z = 4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ < Γ c .
Physical Review B, 2006
We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p * , at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.
Journal of Physics A-mathematical and General, 1994
We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.
Multicanonical Study of the 3D Ising Spin Glass
We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite size scaling, as well as the zero temperature limit to explore the ground state properties.