Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at $T=0,$ with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ${\ensuremath{\sigma}}_{c}=0.64\ifmmode\pm\else\textpm\fi{}0.08.$ Results are compared with existing theories and with the study of metastable avalanches in the same model.Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at $T=0,$ with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ${\ensuremath{\sigma}}_{c}=0.64\ifmmode\pm\else\textpm\fi{}0.08.$ Results are compared with existing theories and with the study of metastable avalanches in the same model.

arXiv:cond-mat/9905188Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsFeb 1, 199934 citations

Universality in two-dimensional Ising models

Henk W. J. Blöte, M. P. Nightingale

Physica A Statistical Mechanics and its ApplicationsDec 1, 198540 citations

First-order phase transition and metastability in the critical two-dimensional Ising model

S. B. Rutkevich

The fermionic version of the two-dimensional Ising model in a uniform magnetic field is studied. Its approximate but rather accurate solution was obtained recently in a variational procedure based on the BCS ansatz for the ground state. Here, this solution is continued analytically into the complex H-plane in the vicinity of the origin. In the ferromagnetic phase an essential singularity in the free-energy is observed at the point H=0 of the type predicted by the droplet condensation theory. Simple phenomenological estimates for the radius of the critical droplet and for the rate of decay of metastable states are confirmed by microscopic calculations.The fermionic version of the two-dimensional Ising model in a uniform magnetic field is studied. Its approximate but rather accurate solution was obtained recently in a variational procedure based on the BCS ansatz for the ground state. Here, this solution is continued analytically into the complex H-plane in the vicinity of the origin. In the ferromagnetic phase an essential singularity in the free-energy is observed at the point H=0 of the type predicted by the droplet condensation theory. Simple phenomenological estimates for the radius of the critical droplet and for the rate of decay of metastable states are confirmed by microscopic calculations.

Journal of Physics A Mathematical and GeneralJun 21, 19953 citations

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Francisco J. Pérez‐Reche, Eduard Vives

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at $T=0$ have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at $T=0$ .Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at $T=0$ have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at $T=0$.

arXiv:cond-mat/0403754Physical Review BDec 20, 200472 citations

Approximate calculations for the two-dimensional Ising model

Frank A. Blood

Journal of Statistical PhysicsDec 1, 19703 citations

Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at

T=0,

with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ${\ensuremath{\sigma}}_{c}=0.64\ifmmode\pm\else\textpm\fi{}0.08.$ Results are compared with existing theories and with the study of metastable avalanches in the same model.

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at

T=0

have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at

T=0