Monte Carlo study of the triangular Blume-Capel model under bond randomness

Abstract

The effects of bond randomness on the universality aspects of a two-dimensional (d = 2) Blume-Capel model embedded in the triangular lattice are discussed. The system is studied numerically in both its first- and second-order phase-transition regimes by a comprehensive finite-size scaling analysis for a particularly suitable value of the disorder strength. 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 two-dimensional (2D) 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 again to the same universality class. Although the first finding reinforces the scenario of strong universality in the 2D Ising model with quenched disorder, the second is in difference from the critical behavior, emerging under randomness, in the cases of the ex-first-order transitions of the Potts model. Finally, our results verify previous renormalization-group calculations on the Blume-Capel model with disorder in the crystal-field coupling.

Magnetic properties of a spin-1 triangular Ising system

“…[9], same system, but different method, namely MCs, is as follows: (1) the system within the EFT shows the tricritical point as well as the tetracritical and critical end special points, but the system within the MCs displays only a tricritical point. (2) Three different ordered phases, namely (1 1 1), ( À 1, À 1, 1), ( À1, 0, 1), is observed when using the EFT, but defines only one ordered phase when using the MCs.…”

“…They also investigated the critical behavior of the corresponding T¼ 0 ferromagnet to spin-glass transition, signaled by a breakdown of the magnetization, using finite-size scaling analyses of the magnetization. The triangular Blume-Capel (BC) model has been studied by using Monte-Carlo simulations (MCs) and discussed that the effects of bond randomness on the universality aspects of a two dimensional BC model embedded in a triangular lattice have been discussed [9]. Žukovič et al [10] examined the effects of selective dilution on the phase diagrams and ground-state magnetizations of the spin-1/2 Ising antiferromagnetic model by using EFT.…”

Topological phase transition of a fractal spin system: The relevance of the network complexity

“…Our theory reproduces qualitatively the results of Chen et al 10 that confirmed, through simulations on a 2D eight-state Potts model, that the presence of randomly distributed ferromagnetic bonds changes the phase transition from first to second order. The same analysis can be applied to results that were obtained by Theodorakis et al 11 with a 2D Blume-Capel model embedded in a triangular lattice, and by Fytas et al 12 for an antiferromagnetic Ising model with next nearest neighbor interactions. And second, we use a qualitative description that suggests how the topological complexity of the network can produce such a phase transition.…”

The Kinetic Spin-1 Ising System on Triangular Lattice: the Effects of Crystal Field and Frequency of Oscillating External Magnetic Field

“…Therefore, there have been increasing numbers of works dealing with the Ising system on a triangular lattice in the very recently literature (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein). We should also Mehmet Ertaş mehmetertas@erciyes.edu.tr 1 Department of Physics, Erciyes University, 38039 Kayseri, Turkey mention that the spin-1 Ising model on triangular lattice has been also studied using the well-known methods in the equilibrium statistical physics, such as the position-space renormalization group methods [17,[38][39][40][41], finite-size scaling analysis [18], twospin cluster effective field theory (EFT) [19], Monte Carlo simulations [20][21][22][23] and EFT with correlation [24] In spite of these studies, in the best of our knowledge, the dynamic phase transitions and dynamic phase diagrams of kinetic Ising system on triangular lattice have not been investigated.…”