Critical exponents of the Ising model with competing Glauber and Kawasaki dynamics

Grandi, B. C. S.; Figueiredo, W.

doi:10.1103/physreve.53.5484

Cited by 29 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kinetic generalizations of the Ising model, for example the Glauber model or the Kawasaki model, are phenomenological models and have been studied extensively [15][16][17][18][19][20]. Combination of the Glauber and the Kawasaki dynamics has been also considered [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries

Khorrami

Aghamohammadi

2002

Phys. Rev. E

View full text Add to dashboard Cite

The Glauber model on a one-dimensional lattice with boundaries (for the ferromagnetic-and anti-ferromagnetic case) is considered. The largetime behaviour of the one-point function is studied. It is shown that, for any positive temperature, the system shows a dynamical phase transition. The dynamical phase transition is controlled by the rate of spin flip at the boundaries, and is a discontiuous change of the derivative of the relaxation time towards the stationary configuration.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries

Khorrami

Aghamohammadi

2002

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The dynamical behavior of the Ising model was successfully described with the Glauber [1] and Kawasaki [2] mechanisms. In the past decades, an interesting problem has been attracting much attention, i.e., the competing Glauber-type and Kawasaki-type dynamics, which leads to non-equilibrium steady states [3][4][5][6]. This competing mechanism has been applied to the other spin models [7][8][9][10] as well, and the emergence of the dynamical tricritical point and self-organization have been reported.…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

2019

View full text Add to dashboard Cite

This article offers a detailed analysis of the Ising model in 2D small-world networks with competing Glauber and Kawasaki dynamics. The non-equilibrium stationary state phase transitions are obtained in these networks. The phase transitions are discussed, and the phase diagrams are obtained via Monte Carlo simulations and finite-size analyzing. We find that as the addition of links increases the phase transition temperature increases and the transition competing probability of tricritical point decreases. For the competition of the two dynamics, ferromagnetic to anti-ferromagnetic phase transitions and the critical endpoints are found in the small-world networks.

show abstract

“…Then there will a competition between the two dynamics. This competing mechanism has been applied to the spin models [13][14][15][16][17][18][19], and interesting self-organization has been reported. All these works have considered regular lattice, and to extend the investigation to the small-world networks should be of interest.…”

Section: Introductionmentioning

confidence: 99%

Small-world network effect in competing Glauber- and Kawasaki-type dynamics

Zhu

Liu

Han

2003

The European Physical Journal B - Condensed Matter

View full text Add to dashboard Cite

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1 − p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.

show abstract

Critical exponents of the Ising model with competing Glauber and Kawasaki dynamics

Cited by 29 publications

References 11 publications

Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries

Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries

Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

Small-world network effect in competing Glauber- and Kawasaki-type dynamics

Contact Info

Product

Resources

About