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Chinese Physics C

A MONTE CARLO RENORMALIZATION GROUP STUDY OF A 2-DIMENSIONAL TRIANGULAR LATTICE

Published Jan 1, 1987• 0 citations
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Abstract

The method developed by D.J.E.Callaway is applied to Ising model on a two-dimen-sional triangular lattice.A fixed point and critical exponent are found.The results are con-sistent with one of the exact theories very well.Obviously this method show superiority tothat obtained by some other approximate methods.The method is also applied to Z_2 gauge theoryon a 2-dimensional triangular lattice,no fixed points are found,in agreement with other me-thods.

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The method developed by D.J.E.Callaway is applied to Ising model on a two-dimen-sional triangular lattice.A fixed point and critical exponent are found.The results are con-sistent with one of the exact theories very well.Obviously this method show superiority tothat obtained by some other approximate methods.The method is also applied to Z_2 gauge theoryon a 2-dimensional triangular lattice,no fixed points are found,in agreement with other me-thods.
The renormalisation group method of Kadanoff is applied to the spin- 1 / 2 Ising model in two dimensions using a transformation applicable to both the square and triangular lattices. Two types of cluster are studied for the triangular lattice.The first cluster yields a new fixed point but the results for the critical temperature and critical exponents are in poor agreement with the known exact values. The second cluster maps directly onto the fixed point found by Kadanoff for the square lattice yielding excellent values for both the critical exponents and the critical temperature.