The three-dimensional site-random Ising model consisting of two types of magnetic ions, A and B, is investigated by means of the exchange Monte Carlo method. The nearest-neighbor interactions are antiferromagnetic (AF) for the B-B pair and ferromagnetic (FM) otherwise. A uniform FM or AF ordering is found to exist in a wide range of concentration c of A ions, in contrast with the bond-random Ising model such as the ± J model. The phase diagram is found to be symmetric on the c – T plane, though the ratio of the FM bonds to AF ones is asymmetric with respect to c =1/2. Spin configurations of degenerate ground states and their cluster structure are also studied. Even in the system with c =0.55, there exists only a unique rigid cluster which includes about 90% of spins and that cluster shows nonvanishing uniform magnetization. These results strongly suggest that the present model has neither a spin glass phase nor an FM-AF mixed phase, though their existence in a quite narrow region around c =1/2 has not been completely excluded yet.
The phase diagram of modified random-bond Ising model has been investigated. The model is based on random-bond Ising model in which the distribution of magnetic interaction is Gaussian rather than the uniform distribution. The center of the distribution is positive so that most of the interactions are ferromagnetic. However the width of the distribution can be varied. The increasing of the width (J) induces disorder to this system. It is expected that when the tail of the distribution reaches the negative interaction region, the system at low temperature shows the cross over between ferromagnetic phase and spin glass phase. By using magnetization and spin glass magnetization, three ordered phases appear in the J-T phase diagram: (1) the ferromagnetic (FM) phase; (2) the spin glass (SG) phase; (3) the paramagnetic (PM) phase. At very high temperature the system is in paramagnetic phase. At low temperature and small distribution the system is in ferromagnetic phase. The cross over between ferromagnetic phase and spin glass phase is visible as the width of the interaction distribution is increase at low temperature. The critical temperature has been obtained by using Binder cumulant of spin glass magnetization.
The phase diagrams and critical properties of a quenched random alloy of a ferromagnet and an antiferromagnet (or of two antiferromagnets with different periodicities) are studied in the mean-field approximation and by renormalization-group techniques in $d=6\ensuremath{-}\ensuremath{\epsilon}$ dimensions, using the $n\ensuremath{\rightarrow}0$ replica method. If only nearest-neighbor interactions are assumed, then one finds ferromagnetic (
F), antiferromagnetic (AF), and spin-glass (SG) phases. As the average strength of the next-nearest-neighbor interactions is increased (e.g., by an additional component in the alloy), the
F and the AF phases approach each other, and one may find regions in parameter space where a mixed
F-AF phase exists, as discussed in Paper II of this series. The phase diagram exhibits lines of multicritical points where the paramagnetic (
P),
F (or AF) and SG phases coexist (
P-SG-
F or
P-SG-AF), or where the
P,
F, and AF phases coexist ($P\ensuremath{-}F$-AF). These lines meet at a new multicritical point, where all four phases coexist (
P-SG-
F-AF). Recent renormalization-group analysis of
P-SG-
F, by Chen and Lubensky, yields complex exponents for the
XY and Heisenberg cases. We show that the phase diagram predicted by that analysis is difficult to understand even for the Ising case. The same method of analysis yields similar difficulties for
P-SG-
F-AF. A modified way to take the limit $n\ensuremath{\rightarrow}0$, which resolves these difficulties, is presented. This modified way still lacks rigorous justification.
Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the other antiferromagnetic. A phase diagram of the ion concentration dependent critical temperature, Tc was deduced. Combined Bethe Peierls approximation and Mean Field theory phase transition results were compared to the results of the present method. An improved accuracy of the approximations of the critical temperatures was observed. The Monte Carlo simulation is thus shown to be a more reliable method for obtaining the physical properties of the random binary two-dimensional Ising system. Keywords: Binary magnetic two-dimensional Ising system, phase transition, Monte Carlo simulations
Large numbers of ground states of the three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ random-bond Ising model are calculated for sizes up to
143 using a combination of a genetic algorithm and cluster-exact approximation. Several quantities are calculated as functions of the concentration p of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of ${p}_{c}=0.222\ifmmode\pm\else\textpm\fi{}0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents \ensuremath{\nu}=1.1\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\beta}=0.2\ifmmode\pm\else\textpm\fi{}0.1 are calculated. The behavior of the distribution of overlaps
P(q) is used to investigate how the spin-glass phase evolves with increasing concentration
p. The spin-glass order is characterized by a broad distribution of overlaps which extends down to
q=0.We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration
p∊[0,1] of antiferromagnetic and $(1\ensuremath{-}p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension
L up to
700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at ${p}_{c}\ensuremath{\sim}0.103$ compared to the concentration ${p}_{n}\ensuremath{\sim}0.109$ at the Nishimori point, which means that the phase diagram of the model exhibits a re-entrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.
The S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain is investigated by the quantum Monte Carlo method. The randomness is only present on the strong bonds taking values of ±2J randomly, and the weak bonds are uniformly antiferromagnetic with J. The model corresponds to the quasi one-dimensional compound, (CH3)2CHNH3Cu(Clx, Br1-x)3, whose ground state interpolates the Haldane state of the F-AF alternating spin chain at x=1 and the singlet-dimer state of the AF-AF alternating spin chain at x=0. The nonequilibrium relaxation function of the staggered magnetic susceptibility exhibits algebraic divergence in the intermediate region of 0.44 ≪ x ≪ 0.87, which explains the experimental observation of the magnetic phase transition. The results suggest that the antiferromagnetic order becomes critical by the randomness of the bond distributions even in the presence of the rich ferromagnetic bonds.