Effects of a Gaussian random field in the Sherrington-Kirkpatrick spin glass

Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

“…However, many di- Certainly, such properties are expected to be properly explained only if one considers a model which takes into account both spin-glass and random-field ingredients. Indeed, the crossover observed in Fe 0.31 Zn 0.69 F 2 was also found in the study of the SK model under a Gaussian random field [38]. On the other hand, the study of the SK model in the presence of a bimodal random field produced interesting results, with first-order phase transitions and tricritical points [39]; such results may be relevant for explaining the first-order phase transitions observed in Fe x Mg 1−x Cl 2 [13].…”

“…From the theoretical point of view these two problems (RFIM and ISG), have been, in most of the cases, studied in separate, with a few exceptions [36][37][38][39][40]. However, many di- Certainly, such properties are expected to be properly explained only if one considers a model which takes into account both spin-glass and random-field ingredients.…”

Spin-1 Hopfield model under a random field

“…For instance, several studies display broad divergences even for the RFIM phase diagram structure [4,[7][8][9]. On the other hand, the effect of RFs on the SG phase has also been investigated [10][11][12][13][14]. In this case, random bond (RB) interaction models with an additional magnetic RF have been considered extensively.…”

“…We follow closely the procedure used in Ref. [43] to calculate the average over the random field, which means that the average over the h i . It can be obtained as,…”

The van Hemmen model in the presence of a random field

“…Recently, the Ising spin glass with random field in the version of the model proposed by Sherrington and Kirkpatrick (SK) [11] has been treated for Gaussian [12] and bimodal [13] distributions (characterized by a mean value H i = 0 and the…”