Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

Abstract

We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update algorithm and re-weighting techniques. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, α/ν, and ν. We find that, contrary of what happens to the spin-1/2 case, this random system does not belong to the same universality class as the regular two-dimensional ferromagnetic model.

Blume–Capel model on directed and undirected small-world Voronoi–Delaunay random lattices

“…In order to estimate the critical temperature we calculate the second and fourth-order Binder cumulants given by eqs. ( 7) and (8), respectively. It is well known that these quantities are independent of the system size and should intercept at the critical temperature 31 .…”

Contact process on a Voronoi triangulation

“…However, Monte Carlo simulations for the q = 3 Potts model [42] as well for the Ising model in 3D [43,44] and for the spin-3/2 Blume-Capel model [45] yield results that contradict the relevance threshold given by the Harris-Luck criterion. Simulation results for nonequilibrium models, viz.…”

Magnetic models on various topologies

“…Models with spin greater than 1/2 have also been treated by Monte Carlo simulations. While for the spin-1 Ising model one also gets the same universality class as for the model on regular lattices [51], the same is not true for the spin-3/2 case, where the critical exponents are different [52].…”