Stability of a crystal-field split spin glass

The Blume-Emery-Griffiths Spin Glass Model

“…In presence of quenched disorder the Hamiltonian (1) implements different models whose rich phase diagrams are not yet fully explored. Some limiting cases include the standard Ising spin glass [7] (µ → ∞; n i = 1 ∀i) and the Ghatak-Sherrington model [8,12,[9][10][11]13] (K = 0). In the particular case of K = −1 we recover the Frustrated Ising Lattice Gas [14,15] that is a version of the Frustrated Percolation model [16], whose properties suggest a possible close connection with the theories of structural glasses [17].…”

Fermionic quantum spin glass transitions

“…Hence a positive mass forq and a negative one for q guarantees stability. A similar system of coupled stability conditions was found for the BEG -model [2] and for a SK -model with crystal field [3]. Analyzing the stability limits one obtains curves of critical spin and charge fluctuations, respectively:…”

“…We derived a fluctuation theory for the tricritical and finite range ISG f ; for T = 0 a Lagrangian of the same structure is obtained for models including transport mechanism by integrating out dynamical degrees of freedom 3 2 and u (0) = 0 denote the bare coefficients at tricriticality. One fourth order term relevant for replica symmetry breaking is kept.…”

Frustrated Blume-Emery-Griffiths model

“…The single indexed quantities are assumed to be independent of the replica index: m α = m and z α = z, ∀α. This leads to: Almeida [17] and by Mottishaw and Sherrington [19] if J 0 = 0 and if there is no quadrupolar coupling. In order to simplify the notation hereafter, we define…”

“…In this section we restrict ourselves to the replica symmetric solution and we derive the lines of instability to locate the phase transitions lines given in section IV -even though the location of these lines may differ in a more advanced treatment. The stability of the replica symmetric solution of the SK model in its integer spin generalisation was examined by Lage and de Almeida [17] and in greater detail by Mottishaw and Sherrington [19]. These works limit their analysis to the disordered integer S spin glass model without a non-zero ferromagnetic mean and without quadrupolar coupling.…”