Phase Transitions And Critical Behavior Of Multilayer Baxter-Wu Models

Since Andrews discovered the critical point of carbon dioxide in experiments and Van der Waals proposed the theory of gas-liquid phase transition,the study of phase transitions and critical phenomena has been for over a hundred years.Superconductivity,superfluidity,BoseEinstein condensation,swarm aggregation and even microbial collective behavior are all related to phase transitions.There are a large number of phase transition phenomena in nature and human society.Understanding the physical mechanism of phase transition and establishing corresponding theories have become one of the important topics in physics research.Onsager solved the two-dimensional Ising model exactly,and found the divergence behavior of the thermodynamic quantities at the critical point of the two-dimensional Ising model.It is a milestone in the study of phase transition and provides a good criterion for the development of phase transition theory and research methods.Later,Wilson introduced renormalization group theory on the basis of scaling theory and scaling transformation,which enabled people to have a more profound and full understanding of phase transitions and critical phenomena.The traditional theory of phase transitions is only valid at the thermodynamic limit,that is,the number of molecules in the system must be infinite.With the emergence and development of computer technology,computer simulation methods are more utilized in statistical physics,among which the most classic Monte Carlo simulation is widely employed to study phase transitions.The spin model plays a pivotal role in the study of phase transitions.It can help us understand the phase transition behavior of the system,develop and improve the methods for studying phase transitions,and play a key role in our understanding of the nature of phase transitions.In this paper,the phase transition and critical behavior of the Baxter-Wu(BW)model on a two-layer triangular lattice with repulsive interactions are investigated mainly by Monte Carlo simulations.And on the basis of the two-layer model,the phase transition of the multilayer BW system is further studied,and the influence of the number of model layers on the phase transition behavior is discussed.The specific research work and conclusions are as follows:The phase transition and critical behavior of the Baxter-Wu(BW)model on a two-layer triangular lattice with interlayer repulsion is investigated by Monte Carlo simulations and single histogram reweighting techniques.The fourth-order energy cumulants and histograms reveal that the system undergoes a continuous phase transition under strong coupling and a pseudofirst-order transition under weak coupling.Via finite size analysis,the phase transition temperatures and critical exponents under different interlayer coupling strengths are obtained.When the coupling is weak,the critical exponent does not show any universal class the system belongs to due to surface effects,but the energy distribution confirms the continuous phase transition at the thermodynamic limit,and it is observed that the critical exponents are very close to the four-state Potts model.As the coupling increases,the pseudo-first-order phase transition behavior disappears,and the critical exponents are consistent with that of the twodimensional four-state Potts model.Based on the two-layer model work,the phase transition of the BW models on multilayer(3,4,5)triangular lattices with interlayer ferromagnetic Ising interactions are investigated using Monte Carlo simulations and single histogram reweighting techniques.Via finite size analysis,pseudocritical exponents for different layer models are obtained.The thermodynamic limit values of the fourth-order energy cumulants of the system are less than 2/3,and the limit values become smaller as the number of layers increases.The distribution of the energy histograms at the thermodynamic limit show the existence of double peaks,indicating that the systems has two metastable states,ferromagnetic and ferrimagnetic state,at the phase transition point,and the double peaks are more obvious with the increase of the number of layers.These phenomena reveal that the system undergoes a first-order phase transition at the thermodynamic limit,and the signal of the first-order phase transition increases as the number of layers increases.Although the obtained pseudocritical exponents do not exhibit typical discontinuous behavior,they also get closer and closer to the values of first-order phase transitions as the number of layers increases.