Fernández Pérez, Luis AntonioMartín Mayor, VíctorSciretti, D.Tarancón, A.2023-06-202023-06-202005-11-100370-269310.1016/j.physletb.2005.09.049https://hdl.handle.net/20.500.14352/51926© 2005 Elsevier B.V. We are indebted with Juan Jesús Ruiz-Lorenzo for discussions. We are grateful to the Barcelona Supercomputing Center, for allowing us to use Mare Nostrum in its installation phase. Isabel Campos was crucial in this respect. About a third of the total simulation time was obtained from the cluster of the Instituto de Biocomputación y Física de Sistemas Complejos, in Zaragoza, and other computing resources of the Departamento de Física Teórica of Universidad de Zaragoza. We acknowledge partial financial support from Ministerio de Educación y Ciencia (Spain) though research contracts BFM2003-08532 and FIS2004-05073.We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.engjournal articlehttp://doi.org/10.1016/j.physletb.2005.09.049http://www.sciencedirect.com/open access5351-73Critical exponentsRenormalization-groupUniversality classMonte-CarloIsing-modelPHI(4) modelRP(2) modelDimensionsHeisenbergMagnets.Física (Física)Física-Modelos matemáticos22 Física