The 3d random field Ising model at zero temperature (original) (raw)
Related papers
Physical Review E, 2011
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random field distribution shape dependencies of the phase diagrams and magnetization curves are investigated for simple cubic, body centered and face centered cubic lattices. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail.
Ground-state numerical study of the three-dimensional random-field Ising model
Physical Review B, 2003
The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.
Physical Review E
We present a numerical study of the critical behavior of the nonequilibrium zero-temperature random field Ising model in two dimensions on a triangular lattice. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations of systems with linear sizes up to L = 65 536, show that the model is in a different universality class than the same model on a quadratic lattice, which is relevant for a better understanding of model universality and the analysis of experimental data.
Nonequilibrium athermal random-field Ising model on hexagonal lattices
Physical review, 2021
We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32 768 × 32 768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.
The random field Ising model in one and two dimensions: A renormalization group approach
Physica A: Statistical Mechanics and its Applications, 1990
We study tile one-and two-dimensional random field [sing models, using a real space renormalization group approach. We consider a bimodai distribution such that the random field assumes the values of + H or -H with probabilities p and 1 -p, respectively (instead of the usual case p = t_,). We obtain the phase diagrams and exponents associated with the uniform (p = 0, 1) and the random field ( p = t ) problems. Our results are consistent with the absence of a spontaneous magnetization for H ~0 and p #0, 1 in d = 1.2 even at zero temperature. We finally discuss the nature of the singularities in the thermodynamics quantities occurring at T= 0 for discrete values of the random field intensity. Wc compare these results with tho~e obtained previously for the dalutc anttferromagnet in a umtorm field using the same approach.
Theory of the Random Field Ising Model
Series on Directions in Condensed Matter Physics, 1997
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.
Phase transition in the 3d random field Ising model
Communications in Mathematical Physics, 1988
We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,d l for the theory isd l ≦2, settling a long controversy on the subject. Our proof is based on an exact Renormalization Group (RG) analysis of the system. This analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of Imry and Ma. The RG acts in the space of Ising models and in the space of random field distributions, driving the former to zero temperature and the latter to zero variance.
Nonequilibrium random-field Ising model on a diluted triangular lattice
Physical Review E, 2015
We study critical hysteresis in the random-field Ising model (RFIM) on a two-dimensional periodic lattice with a variable coordination number z ef f in the range 3 ≤ z ef f ≤ 6. We find that the model supports critical behavior in the range 4 < z ef f ≤ 6, but the critical exponents are independent of z ef f. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.
Critical aspects of the random-field Ising model
The European Physical Journal B, 2013
We investigate the critical behavior of the three-dimensional random-field Ising model (RFIM) with a Gaussian field distribution at zero temperature. By implementing a computational approach that maps the ground-state of the RFIM to the maximum-flow optimization problem of a network, we simulate large ensembles of disorder realizations of the model for a broad range of values of the disorder strength h and system sizes V = L 3 , with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 10 3 . Using well-established finitesize scaling schemes, the fourth-order's Binder cumulant, and the sample-to-sample fluctuations of various thermodynamic quantities, we provide high-accuracy estimates for the critical field hc, as well as the critical exponents ν, β/ν, andγ/ν of the correlation length, order parameter, and disconnected susceptibility, respectively. Moreover, using properly defined noise to signal ratios, we depict the variation of the self-averaging property of the model, by crossing the phase boundary into the ordered phase. Finally, we discuss the controversial issue of the specific heat based on a scaling analysis of the bond energy, providing evidence that its critical exponent α ≈ 0 − .
Physical Review B, 1995
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length ξ diverges with an exponent ν = 1.1 ± 0.2 at the critical temperature and that χ ∼ ξ 2−η with η = 0.50 ± 0.05 for the connected susceptibility and χ dis ∼ ξ 4−η with η = 1.03 ± 0.05 for the disconnected susceptibility. Together with the amplitude ratio A = limT →Tc χ dis /χ 2 (hr/T) 2 being close to one this gives further support for a two exponent scaling scenario implying η = 2η. The magnetization behaves discontinuously at the transition, i.e. β = 0, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.