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Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents

We perform Monte Carlo simulations, combining both the Wang-Landau and the Metropolis algorithms, to investigate the phase diagrams of the Blume-Capel model on different types of nonregular lattices (Lieb lattice (LL), decorated triangular lattice (DTL), and decorated simple cubic lattice (DSC)). The nonregular character of the lattices induces a double transition (reentrant behavior) in the region of the phase diagram at which the nature of the phase transition changes from first-order to second-order. A physical mechanism underlying this reentrance is proposed. The large-scale Monte Carlo simulations are performed with the finite-size scaling analysis to compute the critical exponents and the critical Binder cumulant for three different values of the anisotropy $Δ/J \in \big\{ 0, 1, 1.34 \textrm{ (for LL)}, 1.51 \textrm{ (for DTL and DSC)} \big\}$, showing thus no deviation from the standard Ising universality class in two and three dimensions. We report also the location of the tricritical point to considerable precision: ($Δ_t/J=1.3457(1)$; $k_B T_t/J=0.309(2)$), ($Δ_t/J=1.5766(1)$; $k_B T_t/J=0.481(2)$), and ($Δ_t/J=1.5933(1)$; $k_B T_t/J=0.569(4)$) for LL, DTL, and DSC, respectively.