Eur. Phys. J. B 4, 431-440 (1998)
https://doi.org/10.1007/s100510050400

Phase transition in the Blume-Capel model with second neighbour interaction

¹ Laboratoire de Magnétisme et de Physique des Hautes Énergies, Département de Physique, BP 1014, Faculté des Sciences, Rabat, Morocco
² Laboratoire des Matériaux, des Sciences et Techniques des Énergies Renouvelables, BP 6207, ENSET, Rabat, Morocco

Corresponding author: ^a benyous@fsr.ac.ma

Received: 3 November 1997
Revised: 31 March 1998
Accepted: 7 April 1998
Published online: 15 August 1998

Abstract

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis.