Monte Carlo studies of the Blume–Capel model on nonregular two- and three-dimensional lattices: phase diagrams, tricriticality, and critical exponents
Mouhcine Azhari, Unjong Yu
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>J</mml:mi> <mml:mo>∈</mml:mo> <mml:mfenced close="}" open="{"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1.34</mml:mn> <mml:mspace class="nbsp" width="0.3333em"/> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mtext>for</mml:mtext> <mml:mspace width="thinmathspace"/> <mml:mtext>LL</mml:mtext> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>1.51</mml:mn> <mml:mspace class="nbsp" width="0.3333em"/> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mtext>for</mml:mtext> <mml:mspace width="thinmathspace"/> <mml:mtext>DTL</mml:mtext> <mml:mspace width="thinmathspace"/> <mml:mtext>and</mml:mtext> <mml:mspace width="thinmathspace"/> <mml:mtext>DSC</mml:mtext> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:math> , 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.