Universality of the Ising and the S=1 model on Archimedean lattices: a Monte Carlo determination

Phase transition in the majority-vote model on the Archimedean lattices

The majority-vote model with noise was studied on the 11 Archimedean lattices by the Monte Carlo method and finite-size scaling. The critical noises and critical exponents were obtained with precision. Contrary to some previous reports, we confirmed that the majority-vote model on the Archimedean lattices belongs to the two-dimensional Ising universality class. It was shown that very precise determination of the critical noise is required to obtain proper values of the critical exponents.

Critical phenomena in the majority voter model on two-dimensional regular lattices

In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

Dynamic approach to finite-temperature magnetic phase transitions in the extended J1-J2 model with vacancy order

The recently discovered iron-based superconductors A(y)Fe(2-x)Se(2) (A=K, Rb, Cs, Tl) show a long-range antiferromagnetic order with an unexpectedly high transition temperature T(N)~550 K and a unique √5×√5 vacancy order. Taking the extended J(1)-J(2) model as a minimal model, we investigate the finite-temperature magnetic phase transitions in a square lattice with a √5×√5 vacancy superstructure by using large-scale Monte Carlo simulations. By the parallel tempering technique, the block spin checkerboard and stripe antiferromagnetic states are detected to be the ground states for three representative sets of model parameters. The short-time dynamic approach is applied to accurately determine the critical temperature as well as the static and dynamic exponents. Our results indicate that the dramatic enhancement of the critical temperature as observed in experiments should be mainly due to a combination of the vacancy order and the block lattice contraction.

Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line

We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.

Universality aspects of the d = 3 random-bond Blume-Capel model

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that the second-order transition emerging under bond randomness from the first-order regime of the pure model belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site and bond dilution). The second amounts to a strong violation of the universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.