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Hebei Sheng Kexueyuan xuebao

The real- space renormalization- group research of an ising model with next- nearest- neighbour interactions on kagomé

Zheng Jun-Juan

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

A two-dimensional Ising model with next-nearest-neighbour interactions on Kagome lat- tice is studied by the real-space renormalization-group methods. The critical temperature and expo- nents are obtained.

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We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.
Real space renormalisation group techniques and the replica method of Edwards and Anderson (1975), combined with successive variational approximations going beyond mean field, are used to calculate phase diagrams of various Ising systems. For a bond dilute 2D Ising model with nearest-neighbour interactions, real-space renormalisation group techniques provide very precise results which are used to test the reliability of the replica method. Combined with variational approximations going beyond mean field, this last method is applied to 3D Ising models with competing nearest-neighbour and next-nearest-neighbour interactions.
We investigate the mixed-spin (spin-1/2 and spin-1) antiferromagnetic Ising model in two dimensions through a real-space renormalization group transformation. The model includes nearest and next-nearest neighbor interactions and is suitable to describe ferrimagnetic ordering. We present the finite-temperature phase diagram of the model. The presence of the second-neighbor bonds enlarge the ferrimagnetic phase. Our results do not indicate the existence of a tricritical point, contrary to previous effective-field calculations.