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Dynamic Monte Carlo simulations for a square-lattice Ising ferromagnet with a phonon heat bath

Kyungwha Park, M. A. Novotny

arXiv:cond-mat/0109214Computer Physics CommunicationsAug 1, 20029 citations

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

Kyungwha Park, M. A. Novotny, Per Arne Rikvold

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to d-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches [H]/J=2 at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approach zero under these conditions. Near [H]/J=2 and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for [H]/J>2 and one for [H]/J<2.We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to d-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches [H]/J=2 at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approach zero under these conditions. Near [H]/J=2 and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for [H]/J>2 and one for [H]/J<2.

arXiv:cond-mat/0206329Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsNov 5, 200214 citations

Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

J. Salas

arXiv:hep-lat/9409015Journal of Statistical PhysicsSep 1, 19953 citations

Numerical calculation of the thermodynamic properties of the Ising model on the square lattice

T. Morita

Physica A Statistical Mechanics and its ApplicationsJul 1, 19812 citations

Propagação de danos no modelo de ising em redes de bravais e em fractais

Carlos Argolo Pereira Alves

In this work we have studied, by Monte Carlo computer simulation, several properties that characterize the damage spreading in the Ising model, defined in Bravais lattices (the square and the triangular lattices) and in the Sierpinski Gasket. First, we investigated the antiferromagnetic model in the triangular lattice with uniform magnetic field, by Glauber dynamics; The chaotic-frozen critical frontier that we obtained coincides , within error bars, with the paramegnetic-ferromagnetic frontier of the static transition. Using heat-bath dynamics, we have studied the ferromagnetic model in the Sierpinski Gasket: We have shown that there are two times that characterize the relaxation of the damage: One of them satisfy the generalized scaling theory proposed by Henley (critical exponent z~A/T for low temperatures). On the other hand, the other time does not obey any of the known scaling theories. Finally, we have used methods of time series analysis to study in Glauber dynamics, the damage in the ferromagnetic Ising model on a square lattice. We have obtained a Hurst exponent with value 0.5 in high temperatures and that grows to 1, close to the temperature TD, that separates the chaotic and the frozen phasesIn this work we have studied, by Monte Carlo computer simulation, several properties that characterize the damage spreading in the Ising model, defined in Bravais lattices (the square and the triangular lattices) and in the Sierpinski Gasket. First, we investigated the antiferromagnetic model in the triangular lattice with uniform magnetic field, by Glauber dynamics; The chaotic-frozen critical frontier that we obtained coincides , within error bars, with the paramegnetic-ferromagnetic frontier of the static transition. Using heat-bath dynamics, we have studied the ferromagnetic model in the Sierpinski Gasket: We have shown that there are two times that characterize the relaxation of the damage: One of them satisfy the generalized scaling theory proposed by Henley (critical exponent z~A/T for low temperatures). On the other hand, the other time does not obey any of the known scaling theories. Finally, we have used methods of time series analysis to study in Glauber dynamics, the damage in the ferromagnetic Ising model on a square lattice. We have obtained a Hurst exponent with value 0.5 in high temperatures and that grows to 1, close to the temperature TD, that separates the chaotic and the frozen phases

Aug 6, 19990 citations

Monte Carlo study on phase transition of Ising spin glasses

Koji Fukushima

Jan 1, 19960 citations

Low Temperature Dynamic Monte Carlo Simulations with a Phonon Heat Bath for Square-Lattice Ising Ferromagnets

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