Critical nonequilibrium cluster-flip relaxations in Ising models

At critical points, power-law relaxations are ubiquitously observed. In Monte Carlo simulations using local-update, the understanding of the relations between dynamical and critical exponents enable us to study critical phenomena by observing their power-law relaxations. On the other hand, little is known about relaxations in cluster-flip updates. Recently Nonomura claimed that critical nonequilibrium relaxation of the 2-dimensional Ising model by cluster-flip update is described by the stretched-exponential type [1]. Furthermore our consecutive studies confirmed that the stretched-exponential relaxation is ubiquitous in cluster-flip Monte Carlo simulations [2,3]. To understand the origin of the relaxation, we analyse the 2-, 3-, 4-dimensional, and infinite-range Ising models. While the infinite-range Ising model shows the simple exponential relaxation, the stretched-exponential relaxations are observed in finite dimensional Ising models.

[1] Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014).
[2] Y. Nonomura and Y. Tomita, Phys. Rev. E 92, 062121 (2015).
[3] Y. Nonomura and Y. Tomita, Phys. Rev. E 93, 012101 (2016).