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

Ising Model for Ferromagnetism

Jonathan V. Selinger

Soft and biological matterAug 19, 201517 citations

Ising model on three-dimensional random lattices: A Monte Carlo study

Wolfhard Janke E, Ramon Villanova

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to $128000\ensuremath{\approx}{50}^{3}$ sites which are linked together according to the Voronoi-Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and ${\ensuremath{\varphi}}^{4}$ field theory on three-dimensional regular cubic lattices.We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to $128000\ensuremath{\approx}{50}^{3}$ sites which are linked together according to the Voronoi-Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and ${\ensuremath{\varphi}}^{4}$ field theory on three-dimensional regular cubic lattices.

arXiv:cond-mat/0211446Physical review. B, Condensed matterOct 31, 200231 citations

Simulation of Ferromagnetic Properties for the Two-Dimensional Ising Model

Christopher M. Lemon, Ronald Johns

Bulletin of the American Physical SocietyOct 11, 20080 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.