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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Damage spreading in the mixed spin Ising model

Ce-Jun Liu, H.-B. Schüttler, Jia-Zhen Hu

Published Dec 17, 2001• 4 citations
Publisher

Abstract

We apply the damage spreading technique to study a mixed spin Ising model consisting of spin 1/2 and spin 1 with a crystal field interaction on the square lattice within a kind of Metropolis dynamics. The completely different behavior, depending on the value of the crystal field interaction, strongly suggests there may exist a dynamical tricritical point where the phase transition may change from the second order to the first order for this model.

DOI
10.1103/physreve.65.016114

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We apply the damage spreading technique to study a mixed spin Ising model consisting of spin 1/2 and spin 1 with a crystal field interaction on the square lattice within a kind of Metropolis dynamics. The completely different behavior, depending on the value of the crystal field interaction, strongly suggests there may exist a dynamical tricritical point where the phase transition may change from the second order to the first order for this model.
The dynamics of a mixed spin Ising model with a crystal field on the square lattice are investigated by using the damage spreading technique and Metropolis sampling method.The simulation results reveal that the damage(Hamming distance)shows a very similar temperature dependence to that of the magnetization.The Hamming distance decreases with temperature and there is a critical temperature,beyond which the phase space trajectories of two systems with different initial configurations consist with each other.The critical temperature increases when the strength of the crystal field decreases,and the mixed spin Ising model will degenerate to a standard Ising model under a considerable weak crystal field.The critical temperature decreases to zero continuously as the strength of the crystal filed increases.There is not any first order phase transition observed in the above process and thus no tricritical point exists in this system.
The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as for the Ising model.
The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.
We study damage spreading in the ferromagnetic Ising model, on the square lattice, by performing numerical simulations in the microcanonical ensemble. Although the damage spreads for all temperature values, a dynamical critical phenomenon is observed at Td{\mathit{T}}_{\mathit{d}}Td​=1.020(2)TC{\mathit{T}}_{\mathit{C}}TC​ (TC{\mathit{T}}_{\mathit{C}}TC​ is the Curie temperature): For T\ensuremath{\ge}Td{\mathit{T}}_{\mathit{d}}Td​ the damage D(t) is insensitive to its initial value D(0), while for TTd{\mathit{T}}_{\mathit{d}}Td​ a weak dependence on D(0) is present in such a way that for each T there are two values of D(t) corresponding to the initial conditions D(0)1/2 and D(0)>1/2. We have also identified a convenient order parameter to characterize the transition occurring at Td{\mathit{T}}_{\mathit{d}}Td​. \textcopyright{} 1996 The American Physical Society.