Monte Carlo study of the metamagnet Ising model in a random and uniform field

Abstract

Monte Carlo simulation has been used to determine the phase diagram of a metamagnet Ising model in the presence of a random and uniform magnetic field. The model consists of a spin-1/2 metamagnet in which the nearest neighbor and next nearest neighbor spin interactions are antiferromagnetic (J 1 < 0) and ferromagnetic (J 2 > 0), respectively. We used a bimodal probability distribution for the random magnetic field. We have calculated the staggered magnetization and the fourth-order Binder cumulants in order to obtain the critical points. The phase diagram in the uniform field versus temperature plane presents continuous and first-order transition lines. The phase transition lines, together with the critical and tricritical points, have been obtained for several random field values.

Monte Carlo study of the phase diagram of layered XY antiferromagnet

“…When the strength of the field is increased starting from zero, its phase transition point separating the ordered and disordered phases from each other gets to shift to the lower temperature region. From the theoretical point of view, thermal and magnetic phase transition properties of different kinds of metamagnetic systems have been studied by a wide variety of techniques such as Mean-Field Theory [1][2][3][4][5][6][7][8], Effective-Field Theory [9][10][11][12][13], Monte-Carlo simulation method [14][15][16][17][18][19][20][21][22][23][24][25], and High Temperature Series Expansion method [26,27]. The studies done so far show us that metamagnetic systems can include multicritical points such as tricritical point, bicritical end point and also critical end point depending on the ratio between these ferromagnetic and antiferromagnetic interactions.…”

Random field effects on the phase diagrams of spin-1/2 Ising model on a honeycomb lattice

“…On the other hand, Aharony [11] and Matthis [12] have introduced bimodal and trimodal distributions, respectively and they have reported the observation of tricritical behavior. In order to clarify this controversial situation, the problem have been investigated by a variety of theoretical works such as effective field theory * Electronic address: hamza.polat@deu.edu.tr (EFT) [13][14][15][16][17][18][19][20][21][22][23], Monte Carlo (MC) simulations [24][25][26][27][28][29], mean field (MF) approximation [30][31][32][33][34][35], pair approximation (PA) [36,37], Bethe-Peierls approximation (BPA) [38] and series expandion (SE) [39] method. Moreover, recently phase transition properties of RFIM with symmetric double [40] and triple [41] Gaussian random fields have also been studied by means of a replica method and a rich variety of phase diagrams have been presented.…”