The random field Ising model with an asymmetric trimodal probability distribution

Abstract

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution $P(h_i)=p\delta (h_i-h_0)+q\delta (h_i+h_0)+r\delta (h_i)$, where the probabilities $p,q,r$ take on values within the interval $[0,1]$ consistent with the constraint $p+q+r=1$ (asymmetric distribution), $h_i$ is the random field variable and $h_0$ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of $p,q$ and $h_0$, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to $h_0$.

22 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1304.2525

References in corpus (17)

• 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
• Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
• 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
• First-order transition features of the 3D bimodal random-field Ising model
• Ground state numerical study of the three-dimensional random field Ising model
• First order transition in a three dimensional disordered system
• Destruction of first-order phase transition in a random-field Ising model
• Modified Scaling Relation for the Random-Field Ising Model
• Metamagnets in uniform and random fields
• Multicritical Behavior in a Random-Field Ising Model under a Continuous-Field Probability Distribution
• Wang-Landau study of the critical behaviour of the bimodal 3D-Random Field Ising Model
• Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines
• Diluted Random Fields in Mixed Cyanide Crystals

Cited by in corpus (4)

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• Random-field Ising model: Insight from zero-temperature simulations
• The random field Ising model with an asymmetric and anisotropic trimodal probability distribution
• Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields