On the nature of the phase transition in the three-dimensional random field Ising model

Abstract

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small (bigger than a certain threshold value) the finite temperature phase transition in this system is equivalent to the low-temperature order-disorder transition which takes place at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the function of the strength $h$ of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m(h) for increasing and for decreasing $h$ reveals the hysteresis loop.

arXiv comment22 pages, 12 figures

References in corpus (38)

• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Critical Behavior of Random Bond Potts Models
• Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?
• Critical Exponents of the Three Dimensional Random Field Ising Model
• Critical Exponents of the Three Dimensional Random Field Ising Model
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
• Monte Carlo study of the random-field Ising model
• Scale Invariance in disordered systems: the example of the Random Field Ising Model
• Universality in Three Dimensional Random-Field Ground States
• Spanning avalanches in the three-dimensional Gaussian Random Field Ising Model with metastable dynamics: field dependence and geometrical properties
• Glassy transition in the three-dimensional random field Ising model
• The 3-d Random Field Ising Model at zero temperature
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• New algorithm and results for the three-dimensional random field Ising Model
• High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
• Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2
• Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
• Stability of Random-Field and Random-Anisotropy Fixed Points at large N
• Scaling of the Random-Field Ising Model at Zero Temperature
• New phenomena in the random field Ising model
• Ground states and thermal states of the random field Ising model
• Universality in Random Systems: the case of the 3-d Random Field Ising model
• The random-field specific heat critical behavior at high magnetic concentration: Fe(0.93)Zn(0.07)F2
• Order Parameter Criticality of the d=3 Random-Field Ising Antiferromagnet Fe(0.85)Zn(0.15)F2
• Interactions of several replicas in the random field Ising model
• Random field Ising model: dimensional reduction or spin-glass phase?
• Weak first order transition in the three-dimensional site-diluted Ising antiferromagnet in a magnetic field
• Griffiths singularity in the random Ising ferromagnet
• Phase diagram of the three-dimensional Gaussian random field Ising model: A Monte Carlo renormalization-group study
• Maximal Mean Field Solutions in the Random Field Ising Model: the Pattern of the Symmetry Breaking
• On the thermodynamics of first-order phase transition smeared by frozen disorder
• Nature and number of distinct phases in the random field Ising model
• Non-perturbative phenomena in the three-dimensional random field Ising model
• Monte Carlo Simulation of a Random-Field Ising Antiferromagnet
• Off-perturbative states in disordered systems
• Scaling properties of the critical behavior in the dilute antiferromagnet Fe(0.93)Zn(0.07)F2

Cited by in corpus (9)

• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• First-order transition features of the 3D bimodal random-field Ising model
• Phase Diagram of the 3D Bimodal Random-Field Ising Model
• Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics
• First excitations in two- and three-dimensional random-field Ising systems
• Dimensional Reduction by Conformal Bootstrap
• First-order phase transition in a 2D random-field Ising model with conflicting dynamics
• Low-energy excitations in the three-dimensional random-field Ising model
• Spin-1 Hopfield model under a random field