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
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.
PACS: 05.70.Fh – Phase transitions: general studies / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 75.10.Hk – Classical spin models / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
