Celeste Mendes, Gloria M Buendía, Per Arne Rikvold
{"title":"Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias.","authors":"Celeste Mendes, Gloria M Buendía, Per Arne Rikvold","doi":"10.1103/PhysRevE.110.044133","DOIUrl":null,"url":null,"abstract":"<p><p>We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017)0031-900710.1103/PhysRevLett.118.117202; G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)2469-995010.1103/PhysRevB.96.134306]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)0163-182910.1103/PhysRevB.34.1797]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"110 4-1","pages":"044133"},"PeriodicalIF":2.2000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.044133","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
引用次数: 0
Abstract
We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017)0031-900710.1103/PhysRevLett.118.117202; G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)2469-995010.1103/PhysRevB.96.134306]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)0163-182910.1103/PhysRevB.34.1797]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.
我们对动力学布卢姆-卡佩尔(BC)模型进行了数值研究,以确定它是否表现出之前在超临界时期的动力学伊辛模型中观察到的元磁反常现象 [P. Riego et al.Riego 等人,Phys.118,117202 (2017)0031-900710.1103/PhysRevLett.118.117202;G. M. Buendía 等人,Phys. Rev. B 96,134306 (2017)2469-995010.1103/PhysRevB.96.134306]。我们在一个正方形晶格上采用了热浴蒙特卡洛(MC)算法,在这个晶格中,自旋的取值可以是±1,0,具有非零晶体场,受到正弦振荡场和恒定偏置的作用。在有序区,我们发现在动力学模型和平衡模型之间,有序参数与各自的共轭场具有等效的滞后响应。在无序区(超临界期),我们观察到在易感性和比例方差曲线上有两个与零偏置对称的峰值,这与动力学伊辛模型的数值和实验结果一致。这种行为在平衡模型中并不存在。此外,我们还发现峰值出现在偏置场的较高值上,并且随着零点密度或振荡场振幅的增加而逐渐变小。利用成核理论,我们证明了这些波动与伊辛模型中的波动一样,并非临界现象,而是与单液滴(SD)和多液滴(MD)磁化切换机制之间的交叉有关。对于强(弱)偏压,SD(MD)机制占主导地位。我们还发现,零点集中在液滴表面,与伊辛模型相比,这可能会导致界面张力降低 [M. Schick et al.Schick 等人,Phys. Rev. B 34, 1797 (1986)0163-182910.1103/PhysRevB.34.1797]。我们的研究结果表明,元磁性反常现象并不是动力学伊辛模型所特有的,而是自旋动力学模型的一般特征,并进一步证明了动力学相变与平衡相变之间的等效性仅在临界点附近有效。
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.