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Springer eBooks

Effects of impurities on the ordered phases of one-dimensional systems

Hanoch Gutfreund, W. A. Little

Published Apr 6, 2008• 0 citations
Publisher
DOI
10.1007/3-540-09241-2_42

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The effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional diluted antiferromagnetic three-vertex Potts model on a triangular lattice has been investigated using the Monte Carlo method. The systems with linear dimensions L × L = N and L = 9–144 have been considered. It has been shown using the fourth-order Binder cumulant method that the introduction of a quenched-in disorder into a spin system described by the two-dimensional antiferromagnetic Potts model leads to a change from the first-order phase transition to the second-order phase transition.

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In spin‐gapped quasi‐one‐dimensional antiferromagnets that do not show phase transitions down to zero temperature, impurities cause phase transitions by inducing local magnetic moments around them between which long‐range correlation is mediated by weak interchain couplings. We investigate the difference between the effects of non‐magnetic impurities and those of spin‐1/2 magnetic ones in the impurity‐induced transition temperatures and the staggered magnetization in the impurity‐induced ordered phase by the quantum Monte Carlo method. We find that the staggered correlation induced by spin‐1/2 impurities grows slower than that done by non‐magnetic ones as the system is cooled and approaches the ground state, while the transition temperature induced by the former is higher than that done by the latter. We argue that this is one of the characteristic aspects of the order‐by‐disorder phenomena in quantum systems.
The Wolff cluster Monte Carlo algorithm is used to investigate the effect of frozen nonmagnetic canonically distributed impurities on the phase transitions in a two-dimensional Potts model with the spin state q = 5. Systems with linear dimensions L = 20–160 at spin concentrations p = 1.0 and 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram analysis method it is shown that if a weak quenched disorder in the form of non-magnetic impurities (p = 0.9) is introduced in the system, the first-order phase transition changes to a second-order phase transition.
The effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional diluted antiferromagnetic three-vertex Potts model on a triangular lattice has been investigated using the Monte Carlo method. The systems with linear dimensions L × L = N and L = 9–144 have been considered. It has been shown using the fourth-order Binder cumulant method that the introduction of a quenched-in disorder into a spin system described by the two-dimensional antiferromagnetic Potts model leads to a change from the first-order phase transition to the second-order phase transition.