Hamiltonian studies of the Blume-Emery-Griffiths model

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Abstract
Finite-size scaling methods are used to obtain the phase diagram of the Blume-Emery-Griffiths model in its time-continuous Hamiltonian version. In particular, we locate the tricritical point, where a first-order transition changes to one of second order, and evaluate its exponents. The exponents are in complete agreement with Nienhuis’ conjecture. We also discuss a recent conjecture concerning the universality of the ratio of mass-gap amplitudes. Our results suggest the validity of this conjecture even at the tricritical point.