Numerical study of the random field Ising model at zero and positive temperature

Abstract

In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent $\alpha$ is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp peaks are present in these physical quantities for some realizations of systems sized $16^3$ and larger. These sharp peaks result from flipping large domains and correspond to large discontinuities in ground state bond energies. Finally, zero temperature and positive temperature spin configurations near the critical line are found to be highly correlated suggesting a strong version of the zero temperature fixed point hypothesis.

11 pages, 14 figures

References in corpus (21)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• 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
• Finite Size Scaling analysis of the avalanches in the 3d Gaussian Random Field Ising Model with metastable dynamics
• Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
• Monte Carlo study 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
• 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
• Ground states and thermal states of the random field Ising model
• Ground state numerical study of the three-dimensional random field Ising model
• Modified Scaling Relation for the Random-Field Ising Model
• Ground states versus low-temperature equilibria in random field Ising chains
• Random field Ising systems on a general hierarchical lattice: Rigorous inequalities

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