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Using Monte Carlo simulations, we compute the spin stiffness of a site-random 3d Heisenberg model with competing ferromagnetic and antiferromagnetic interactions. Our results for the pure limit yield values of the the critical temperature and the critical exponent ν in excellent agreement with previous high precision studies. In the disordered case, a mixed "chiral" phase is found which may be in the same universality class as 3d Heisenberg spin glasses.PACS numbers: 64.70. Pf, 75.40.Gb, 75.40.Mg The critical behavior of magnetic systems with quenched disorder has been of considerable theoretical and experimental interest for over 30 years. Disorder can lead to a competition between two order parameters and to a phase diagram which has regions in which each one orders independently as well as a mixed phase where both order simultaneously. These phases often meet at multicritical points and can have various properties which depend on the spin dimensionality. Aharony 1 has recently reviewed some of the old and new results on multicritical points with special attention to high-T c materials. However, the role played by quenched randomness remains a open question.Early renormalization group studies of systems with isotropic interactions and quenched disorder indicated that competing phases existed with multicritical points described by complex exponents 2 or the absence of a stable fixed point 3 . Various scenarios were suggested which included first order transitions, smeared transitions or spin glass ordering. For many years it was believed that a spin glass phase does not exist in 3d XY and Heisenberg systems. However, numerical studies 4 during the last decade have suggested that chiral degrees of freedom are important in spin glasses which have continuous degrees of freedom. More recent work 5,6 indicates that Heisenberg systems exhibit a finite temperature spin glass transition in three dimensions where both the spin and chiral degrees of freedom order simultaneously. The correlation length critical exponent is estimated to be ν = 1.1(2) which differs substantially from that of the pure 3d Heisenberg ferromagnet.In the present work we report a finite size scaling study of the spin stiffness of a 3d site random isotropic Heisenberg model introduced previously by Matsubara et. al.7 . The model describes a mixture of A and B magnetic ions randomly distributed at the sites of a simple cubic lattice with concentrations p and 1 − p respectively. The exchange bonds between neighboring ion pairs are defined so that +J, −J, and +J correspond to A − A, B − B, and A−B (or B −A) pairs respectively. The Hamitonian can be written aswhere) represents a classical three component spin of unit magnitude located at each site i and ε i = 1 or −1 for A or B ions respectively. The average value of ε i over the lattice is < ε i >= 2p−1. As discussed by the previous authors, the Hamiltonian has a symmetry with respect to p and (1 − p) and hence the phase diagram is symmetric about p = 0.5 as shown schematically in Fig. 1 of their ...

Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that XY antiferromagnetic systems undergo a (weak) first order phase transition.