One-Dimensional Time-Dependent Ising Model in an External Magnetic Field

• Authors: M. Błaszyk
• Languages of publication: EN

Abstracts

EN

The relaxation process, through which the inequilibrium state described by the Ising model reaches the equilibrium state, was proposed. The process is defined by the action of the transition matrix on the vector of state and the demand of its normalisation. It is assumed that in the state of inequilibrium the vector of state has the same functional dependence as the eigenvector of the transition matrix corresponding to the highest eigenvalue. Two cases are considered: when the cell under transformation is composed of one or two sites. The calculations were performed for a uniform initial state. For the two cases of one and two-site cells the modes of reaching the equilibrium state via magnetisation were compared. When the external magnetic field and temperature tend to zero, both magnetisation and the correlation function of the nearest neighbours show the critical slowing down phenomenon.

Keywords

EN

05.50.+q

Discipline

• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2009
• Volume: 115
• Issue: 3
• Pages: 617-621

Dates

published

2009-03

received

2008-05-19

Contributors

author

M. Błaszyk

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

• 1. K. Kawasaki, in: Phase Transitions and Critical Phenomena, Eds. C. Domb, M.S. Green, Vol. 2, Academic, New York 1972, p. 443
• 2. S. Wolfram, Rev. Mod. Phys. 55, 601 (1983) Eds. C. Domb, M.S. Green, Vol. 2, Academic, New York 1972.
• 3. E. Domany, W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)
• 4. L.E. Reichl, A Modern Course in Statistical Physics, Edward Arnold Ltd, University of Texas Press, Austin 1980, p. 193
• 5. M. Błaszyk, Acta Phys. Pol. A 107, 451 (2005)

Identifiers

DOI

10.12693/APhysPolA.115.617