Multicritical Bifurcation and First-order Phase Transitions in a Three-dimensional Blume-Capel Antiferromagnet

Abstract

We present a detailed study by Monte Carlo simulations and finite-size scaling analysis of the phase diagram and ordered bulk phases for the three-dimensional Blume-Capel antiferromagnet in the space of temperature and magnetic and crystal fields (or two chemical potentials in an equivalent lattice-gas model with two particle species and vacancies). The phase diagram consists of surfaces of second- and first-order transitions that enclose a ``volume'' of ordered phases in the phase space. At relatively high temperatures, these surfaces join smoothly along a line of tricritical points, and at zero magnetic field we obtain good agreement with known values for tricritical exponent ratios [Y. Deng and H.W.J. Bl{ö}te, Phys. Rev. E {70}, 0456111 (2004)]. In limited field regions at lower temperatures (symmetric under reversal of the magnetic field), the tricritical line for this three-dimensional model bifurcates into lines of critical endpoints and critical points, connected by a surface of weak first-order transitions {inside} the region of ordered phases. This phenomenon is not seen in the two-dimensional version of the same model. We confirm the location of the bifurcation as previously reported [Y.L. Wang and J.D. Kimel, J. Appl. Phys. {69}, 6176 (1991)], and we identify the phases separated by this first-order surface as antiferromagnetically (three-dimensional checker-board) ordered with different vacancy densities. We visualize the phases by real-space snapshots and by structure factors in the three-dimensional space of wave vectors.

arXiv comment18 pages, 20 figures. Accepted for PRE

References in corpus (14)

• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• Underpotential deposition of Cu on Au(111) in sulfate-containing electrolytes: a theoretical and experimental study
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• Fourth-Order Cumulants to Characterize the Phase Transitions of a Spin-1 Ising Model
• Coexistence Curve Singularities at Critical End Points
• Parallel multicanonical study of the three-dimensional Blume-Capel model
• Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement
• The surprising convergence of the Monte Carlo renormalization group for the d=3 Ising Model
• Monte Carlo Simulations of the Critical Properties of a Ziff-Gulari-Barshad model of Catalytic CO Oxidation with Long-range Reactivity
• Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior
• High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model
• Charged Ising Model of Neutron Star Matter
• Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

Cited by in corpus (2)

• Numerical Simulation of a Two-Dimensional Blume-Capel Ferromagnet in an Oscillating Magnetic Field with a Constant Bias
• A comparative review of recent results on supercritical anomalies in two-dimensional kinetic Ising and Blume-Capel ferromagnets