Random-field Blume-Capel model: Mean-field theory

Abstract

The global phase diagram of the Blume-Capel model in a random field obeying the bimodal symmetric distribution is determined by using the mean-field method. The phase diagram includes an isolated ordered critical end point and two lines of tricritical points. A new phase emerges for strong enough random fields: the ferromagnetic-nonmagnetic phase. It is argued that such a phase occurs in three dimensions.

Phase Diagrams and Tricritical Behavior of Spin-2 Ising Model with a Transverse Crystal Field

“…The spin-1 Ising model with longitudinal crystal field has been widely investigated by various techniques: molecular field approximation [2,3], high-density expansion method [4], a new type of cluster theory [5,6], effective field theory with differential operator technique [7,8], linear chain approximation [9], constant coupling [10], cluster variational method in pair approximation [11±13], and the renormalization group technique [14]. This Ising model has successfully been used to describe a great variety of physical systems, such as pure and disordered magnetic systems [15] as well as special magnetic materials (or molecular-based magnetic materials [16,17], surfaces [18] and multilayers [19]).…”

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

“…Another similarly interesting candidate, not yet as much studied in the random-bond version, is the 2d Blume-Capel (BC) model [31,32]. We may note here that most of the existing literature on the BC model with randomness concerns randomness applied to the crystal field and/or spin glass exchange interactions [33][34][35][36]. As it is well known, the pure version of the BC model undergoes an Ising-like continuous phase transition to an ordered ferromagnetic phase as the temperature is lowered for crystal-field couplings less than a tricritical value and a first-order transition for larger values of the crystal-field coupling.…”

The diluted mixed spin‐1/2 and spin‐3/2 Ising model in a longitudinal random field

“…i.e. the transverse Ising model [23][24][25][26][27][28][29][30], the amorphous Ising ferromagnet [31], the site-dilute Ising model [32,33], the semi-infinite Ising model [34], the decorated Ising model [35] and the Blume-Capel model [36]. On the other hand, some authors [37,38] extended the study of the randomfield effects to the spin-3/2.…”