2015/03/10 by Miguel Ruiz-García, M Ruiz-Garcia, L. L. Bonilla +3
Materials Science · Physics and Astronomy · #Antiferromagnetism #Condensed matter physics #Ferromagnetism #Glauber #Hexagonal lattice #Ising model #Lattice (music) #Magnetic field #Magnetization #Material Dynamics and Properties #Materials science #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Random lasers and scattering media #Spins #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech #k-nearest neighbors algorithm
paper · pdf · doi:10.1088/1742-5468/2015/05/p05015
published as Journal of Statistical Mechanics: Theory and Experiment (2015) 05015 · accepted for publication in JSTAT
arxiv created 2015/03/10 · openalex publication_date 2015/05/18 · arxiv updated 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A system of atoms connected by harmonic springs to their nearest neighbors on a lattice is coupled to Ising spins that are in contact with a thermal bath and evolve under Glauber dynamics. Assuming a nearest-neighbor antiferromagnetic interaction between spins, we calculate analytically the equilibrium state. On a one-dimensional lattice, the system exhibits first and second order phase transitions. The order parameters are the total magnetization and the number of spin pairs in an antiferromagnetic configuration. On a hexagonal two dimensional lattice, spins interact with their nearest-neighbors and next-nearest-neighbors. Together with the coupling to atoms, these interactions produce a complex behavior that is displayed on a phase diagram. There are: ordered phases associated to ripples with atomic wavelength and antiferromagnetic order, ordered phases associated to ripples with nanometer wavelengths and ferromagnetic order including phases presenting overall buckling of the lattice, disordered glassy phases, and other phases presenting stripes formed by different domains. These static phases are discussed in relation to existing experiments and results for other models found in the literature.