The random field Ising model with an asymmetric and anisotropic trimodal probability distribution

Ioannis A. Hadjiagapiou

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 13, 3541-3555

Abstract: The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution P(hi)=pδ(hi−h0)+qδ(hi+λ∗h0)+rδ(hi), is investigated. The partial probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1; asymmetric distribution, hi is the random field variable with basic absolute value h0 (strength); λ is the competition parameter, which is the ratio between the respective strength of the random magnetic field in the two principal directions (+z) and (−z) and is positive so that the random fields are competing, anisotropic distribution. 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 mainly second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions joined smoothly by a tricritical point; occasionally, two tricritical points appear implying another second order phase transition. In addition to these points, re-entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of λ, p and q. Using the variational principle, we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h0, considered as an independent variable in addition to the temperature.

Keywords: Ising model; Asymmetric trimodal random field; Anisotropic interactions; Phase-diagram; Tricritical point; Phase transitions (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437112001239
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:13:p:3541-3555

DOI: 10.1016/j.physa.2012.02.007

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().