Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique - art. no. 014418

In this work we generalize and subsequently apply the effective-field renor malization-group (EFRG) technique to the problem of ferro- and antiferromag netically coupled Ising spins with local anisotropy axes in geometrically f rustrated geometries (kagome and pyrochlore lattices). In this framework, w e calculate the various ground states of these systems and the correspondin g critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-orde red state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in th ese systems. In addition, the recently introduced generalized constant coup ling method is also applied to the calculation of the critical points and g round-state configurations. Again, a very good agreement is found with exac t, Monte Carlo, and renormalization-group calculations for the critical poi nts. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which c orrelations outside a frustrated unit are neglected, and scaling is substit uted by strict equality of the thermodynamic quantities.