Numerical evidence of a critical line in the 4d Ising spin glass (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 behaviour of the four-dimensional spin glass in magnetic field
Journal of Physics A: Mathematical and General, 1998
We present numerical simulations of the 4D Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite size effects, suggest the existence of a spin glass phase transition. We present a preliminar determination of critical exponents. We discuss spin glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite size effects, and the behavior of the disorder dependent and of the integrated probability distribution.
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 .
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 .
Quantum critical behavior of a three-dimensional Ising spin glass in a transverse magnetic field
Physical Review Letters, 1994
The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent ν = 1/2 violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc = 0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z = 1.67(6), ν = 0.90(5), β/ν = 1.09(3), and γ/ν = 2.50(3). The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.
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.
Subextensive Singularity in the 2D ± J Ising Spin Glass
Journal of Statistical Physics, 2007
The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for L × L square lattices with L ≤ 48, and p = 0.5, where p is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of L, in order to obtain the low temperature behavior of the model. For large finite L there is a range of T in which the heat capacity is proportional to T 5.33±0.12 . The range of T in which this behavior occurs scales slowly to T = 0 as L increases.
Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field
Physica A: Statistical Mechanics and its Applications, 1998
We study the four dimensional (4D) ±J Ising spin glass in a magnetic field by using the simulated tempering method recently introduced by Marinari and Parisi. We compute numerically the first four moments of the order parameter probability distribution P (q). We find a finite cusp in the spinglass susceptibility and strong tendency to paramagnetic ordering at low temperatures. Assuming a well defined transition we are able to bound its critical temperature.