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

TL;DR

This study uses Monte Carlo simulations to explore phase diagrams, critical behavior, and tricritical points of the Blume-Capel model on nonregular lattices, revealing reentrant transitions and confirming Ising universality.

Contribution

It provides detailed phase diagrams, critical exponents, and tricritical points for the Blume-Capel model on nonregular lattices, highlighting reentrant behavior and universality class consistency.

Findings

Reentrant phase transitions observed on nonregular lattices.

Critical exponents match the Ising universality class.

Precise locations of tricritical points determined.

Abstract

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 $\Delta/J \in \big\{ 0, 1, 1.34 \textrm{ (for LL)}, 1.51 \textrm{ (for DTL and DSC)} \big\}$, 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: ($\Delta_t/J=1.3457(1)$; $k_B T_t/J=0.309(2)$), ($\Delta_t/J=1.5766(1)$; $k_B T_t/J=0.481(2)$), and ($\Delta_t/J=1.5933(1)$; $k_B T_t/J=0.569(4)$) for LL, DTL, and DSC, respectively.