The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$ , with $a \ge 0$ . The critical exponents $γ/ν$ , $β/ν$ , and $ν$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$, with $a \ge 0$. The critical exponents $γ/ν$, $β/ν$, and $ν$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.

arXiv:cond-mat/0509303Sep 12, 20050 citations

Critical behavior of the Ising model on a lattice with fractional space dimension

Chao Fang, Maoxin Liu, Helmut G. Katzgraber

Bulletin of the American Physical SocietyMar 7, 20190 citations

J

varies with the distance

r

between the first neighbors as

J(r) \propto e^{-ar}

, with

a \ge 0

. The critical exponents

γ/ν

β/ν

, and

ν

are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.