Eur. Phys. J. B 44, 309-315 (2005)
https://doi.org/10.1140/epjb/e2005-00130-7

Efficiency of the microcanonical over-relaxation algorithm for vector spins analyzing first and second order transitions

Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Corresponding author: ^a Damien.Loison@physik.fu-berlin.de

Received: 22 September 2004
Revised: 28 January 2005
Published online: 28 April 2005

Abstract

We simulate vectorial spin systems solely with the microcanonical over-relaxation algorithm where the temperature is calculated by a formula of Nurdin and Schotte. We show that this procedure is the most efficient local algorithm besides the nonlocal cluster algorithm not only for first order transitions but also for second order ones. A comparison is made with the Metropolis, heat bath, multicanonical and the Creutz's demon algorithms. We study, using these algorithms, the frustrated J₁-J₂ model on a cubic lattice for XY, Heisenberg and O(4) spins. These models have a breakdown of symmetry for the number of spin components leading to transitions of first order. We show that they are strongly first order. Then, to test the over-relaxation update for second order transitions, we study a ferromagnet on a cubic lattice and a frustrated antiferromagnet on a stacked triangular lattice. We finally point out the advantages and the flaws of the over-relaxation procedure.