Relaxation times in a finite Ising system with random impurities

D.V. Spirin, V. N. Udodov

In recent decades, one-dimensional (quasi-one-dimensional) Ising magnetic compounds have been synthesized, on which new promising materials are based. Here, percolation effects are considered in the model of a one-dimensional Ising magnet of finite nanometer size with boundary conditions “dangling ends”. The model takes into account the interaction with an external magnetic field, nearest-site interaction of nodes, interaction of second and third neighbors, as well as four-particle interactions. To model the phase transition, the Metropolis algorithm was used. Two options for the localization of a nonmagnetic impurity are considered: with mobile impurities and with fixed impurities (frozen impurities). For mobile impurities, the Metropolis algorithm contains the possibility of moving non-magnetic nodes along the chain. In the second variant, when the initial configurations are formed, nonmagnetic impurities in the magnet take random constant equiprobable positions. It is shown that the presence of non-magnetic nodes leads to a weakening of the correlation inside the chain and the magnet breaks up into several parts unconnected by magnetic interaction. The fraction of nonmagnetic atoms, in which the magnet is divided into two non-correlating parts, is an analogue to the percolation threshold in the percolation site problem. The percolation radius corresponds to the farthest nonzero interaction. The paper shows the existence of a relationship between the percolation threshold and the dependences of the relaxation time of the ferromagnet — antiferromagnet phase transition and the dynamic critical exponent Z on the fraction of nonmagnetic impurities in the model of a one-dimensional Ising magnet with fixed (frozen) nonmagnetic impurities. In the case of mobile nonmagnetic impurities, the absence of a clear connection between the percolation threshold and the dependences of the relaxation time and the dynamic critical exponent is shown.

Markus Siegert, Dietrich Stauffer

A. L Talapov, Щур Лев Николаевич

High-accuracy Monte Carlo simulation results for a 1024 * 1024 Ising system with ferromagnetic impurity bonds are presented. The spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since the critical temperature for the system with impurities is almost two times lower than pure Ising T c . Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.

Y Achiam

K. Sawada, Takeo Osawa

Talapov, A L, Щур Лев Николаевич

High accuracy Monte Carlo simulation results for 1024*1024 Ising system with ferromagnetic impurity bonds are presented. Spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since a critical temperature for the system with impurities is almost two times lower than pure Ising T.sub(c). Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.