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Chinese Physics C

A MONTE CARLO RENORMALIZATION GROUP STUDY OF ISING MODEL ON RANDOM TRIANGLE LATTICE

Weichuan Huang

Published Jan 1, 1987• 0 citations
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Abstract

A usual majority rule and a new block method are applied to Ising model on two-dimen-sional random triangle lattice.Either of them has got a good critical exponent.The newblock method has an advantage of easily extending to higher dimensional random lattice.

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Physical Review E•Apr 18, 2005•4 citations
We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.