Numerical study of the spin-3/2 Ashkin-Teller model

The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical properties are recovered, namely the second order transition and multicritical points. The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential. This model shows a new high temperature partially ordered phase, called $\langle S\rangle$ and a new Baxter 3/2 ground state which do not exist either in the spin-1/2 ATM or in the spin-1 ATM.Comment: 8 pages, 8 figure

Steps roughening in thermal relaxation and low-coverage growth of sloped Pt(110) and Ir(110) surfaces: A numerical study

AbstractThe dynamical roughening of [001] steps on sloped Pt (110) and Ir (110) surfaces is investigated by kinetic Monte Carlo simulations. Our model includes deposition, diffusion and fully reversible aggregation on these surfaces with both anisotropic barriers and anisotropic attachment. The barriers for the diffusion processes have been calculated by means of classical molecular dynamics simulations where both metals are modeled by realistic many-body potentials. The roughness is evaluated through calculations of the step width in thermal relaxation of the surface and low-coverage growth conditions. Results indicated a non-trivial behavior of the width in time during relaxation. In growth, power-law behavior is recovered for both metal surfaces. Defects population on terraces is investigated through calculations of adatom and island densities. It is found that at very low temperature (T = 200K for Pt and 400K for Ir and below), a power-law behavior with the growth time is got. Beyond, fluctuations in generated data become important and do not allow to correctly access the true trend of both quantities. Their behavior with the diffusion length at low temperature is singled out

Mapping of (1+1) D-Crystal Growth onto a 14-Vertex Model

A restricted solid-on-solid (SOS) single- and double-step model is introduced and studied with Glauber dynamics. Kinetics and roughness of the growing crystal are described in terms of a Markov process whose states are given by the crystal upper edge profile that we map onto a 14-vertex model. We solve exactly the kinetic equation for small-size versions of the model. Extensive simulations are performed to derive the large scale properties. The present study appears as a further extension of Gates and Westcott's investigation of the single-step model

Effects of the random single-ion anisotropy on the spin-1 Blume-Emery-Griffiths model

© 2021 Elsevier B.V.The Blume-Emery-Griffiths (BEG) model is considered on the Bethe lattice (BL) in terms of exact recursion relations (ERR) under the effect of a crystal field (D) which was either turned on or off randomly for a given probability. The repulsive case of biquadratic exchange interaction ((K < 0)) between the nearest-neighbor (NN) spins is assumed and the effects of changing the coordination number are also investigated. The thermal variation of the order-parameters, i.e. dipole and quadrupole moments, is examined to obtain the phase diagrams. Very rich phase diagrams with the second- and first-order phase transition lines, tricritical, bicritical and critical end points and the occurrence of reentrant behavior are observed. Different phase regions were explored which include the ferromagnetic (F), paramagnetic (P), staggered quadrupolar (SQ) and ferrimagnetic (FI) phases

Effective field theory study of bond dilution effects on transverse Ising antiferromagnet in a random longitudinal magnetic field

The transverse antiferromagnetic spin-[Formula presented] Ising model is studied within the effective field theory with correlations for a finite cluster with random bond dilution and random longitudinal magnetic field effects. The bonds are either randomly antiferromagnetically switched on with probability p or switched off with 1−p. In addition, the external magnetic field is randomly turned up or down in the longitudinal direction with probability t and 1−t, respectively. The thermal variations of the longitudinal and transverse sublattice magnetizations, as well as the staggered longitudinal magnetizations with coordination numbers q=4 and 6, are studied to obtain the phase diagrams of the model. It is found that the model exhibits both first- and second-order phase transitions. Compensation temperatures and reentrant behaviors are also shown for appropriate values of the system parameters

Interplay between spin-crossover and magnetic interactions in a BEG model

A two-dimensional Blume-Emery-Griffiths spin-1 model with spin-phonon interaction is introduced to investigate the thermodynamic properties of Prussian Blue Analogs and Spin-crossover materials. The quadrupolar interaction parameter is assumed to depend on the temperature in the form K = αkBT while the crystal-field depends both on the ligand-field strength and the degeneracy ratio between high spin (HS) and low spin (LS) states as in some previous works. The model is solved by means of two statistical-mechanical methods: kinetic Monte Carlo simulations and corrective effective field theory calculations. Our calculations indicate that by tuning α, the spin-crossover transition changes to a sharp first order transition where the HS fraction, nHS changes discontinuously. Second order transitions are observed in the presence of magnetic ordering when the nearest-neighbor coupling constant J exceeds some critical value Jc which depends on α and other model parameters. Below Jc, simple spin-transition occurs at an equilibrium temperature Teq that is very sensitive to the values of the degenaracy ratio and the ligand-field. Competition between model parameters lead to interesting phase diagrams. Some of them are displayed for varying values of the coupling J and also in the specific case where J and K are of the same order of magnitude. Thermal hysteresis loops have been calculated by Monte Carlo simulations and also by using the self-consistent equations in the case of long-lived metastable states showing strong dependence on model parameters