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Physical review. E

Hamiltonian short-time critical dynamics of the three-dimensional XY model

LIVIA CAROLINA DE SOUZA, Adauto J. F. de Souza, M. L. Lyra

Published May 6, 2019• 7 citations
Publisher

Abstract

The short-time relaxation critical behavior of the XY model on a simple-cubic lattice is investigated within the scope of deterministic Hamiltonian dynamics. The Hamiltonian includes a first-neighbor interaction between planar vectors and a rotational kinetic term from which the motion equations are derived. The dynamical evolution from a fully ordered initial state is followed by employing a symplectic algorithm based on a high-order Trotter-Suzuki decomposition of the time-evolution operator. A finite-time scaling analysis is performed to provide accurate estimates of the critical energy density, the order-parameter relaxation exponent, and the dynamical critical exponent. The estimated critical exponents are consistent with prior theoretical and experimental values reported for the superfluid ^{4}He, extreme type-II superconducting, and Bose-Einstein condensation transitions.

DOI
10.1103/physreve.99.052104

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The short-time relaxation critical behavior of the XY model on a simple-cubic lattice is investigated within the scope of deterministic Hamiltonian dynamics. The Hamiltonian includes a first-neighbor interaction between planar vectors and a rotational kinetic term from which the motion equations are derived. The dynamical evolution from a fully ordered initial state is followed by employing a symplectic algorithm based on a high-order Trotter-Suzuki decomposition of the time-evolution operator. A finite-time scaling analysis is performed to provide accurate estimates of the critical energy density, the order-parameter relaxation exponent, and the dynamical critical exponent. The estimated critical exponents are consistent with prior theoretical and experimental values reported for the superfluid ^{4}He, extreme type-II superconducting, and Bose-Einstein condensation transitions.
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The critical relaxation from the low-temperature ordered state of the three-dimensional Ising model with competing interactions on a simple cubic lattice has been studied for the first time using the short-time dynamics method. Competition between exchange interactions is due to the ferromagnetic interaction between the nearest neighbors and the antiferromagnetic interaction between the next nearest neighbors. Particles containing 262144 spins with periodic boundary conditions have been studied. Calculations have been performed by the standard Metropolis Monte Carlo algorithm. The static critical exponents of the magnetization and correlation radius have been calculated. The dynamic critical exponent of the model under study has been calculated for the first time.
The critical relaxation from the low-temperature ordered state of the three-dimensional fully frustrated Ising model on a simple cubic lattice has been studied using the short-time dynamics method. Particles with the periodic boundary conditions containing N = 262144 spins have been studied. Calculations have been performed by the standard Metropolis Monte Carlo algorithm. The static critical exponents of the magnetization and correlation radius have been obtained. The dynamic critical exponent of the model under study has been calculated.
Critical relaxation from the low-temperature ordered state of the three-dimensional fully frustrated Ising model on a simple cubic lattice is studied by the short-time dynamics method. Cubic systems with periodic boundary conditions and linear sizes of L = 32, 64, 96, and 128 in each crystallographic direction are studied. Calculations were carried out by the Monte Carlo method using the standard Metropolis algorithm. The static critical exponents for the magnetization and correlation radius and the dynamic critical exponents are calculated.
We present extensive Monte Carlo spin-dynamics simulations of the vector Blume-Emery-Griffiths model with three-dimensional spins on a simple cubic lattice and periodic boundary conditions. For a range of Hamiltonian parameters, this model reproduces the phase diagram topology of the one experimentally observed for bulk mixtures of 3He-4He . Highly efficient decomposition time integration algorithms have been used to obtain the evolution of the equations of motion from which we have computed the dynamic structure factor S(q,omega) close to critical and tricritical points. The dispersion relation and the corresponding dynamic exponents have been obtained in the critical and multicritical transitions. We find that the dynamic critical exponents for in-plane and out-of-plane fluctuations are the same at the tricritical point but are in fact different along the critical line.
The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for P greater, similar 0.03.