The Higgs boson has an important role in the theoretical formulation of the standard model of fundamental interactions. Symmetry breaking of the vacuum via the Higgs field allows the gauge bosons of the weak interaction and all fermions to acquire mass in a way that preserves gauge-invariance, and thus renormalizablility. The Standard Model can accommodate an arbitrary number of Higgs fields with appropriate charge assignments. To explore the effects of multiple Higgs particles, the SU(2)-multi-Higgs model is studied using lattice simulations, a non-perturbative technique in which the fields are placed on a discrete space-time lattice. The formalism and methods of lattice field theory are discussed in detail. Standard results for the SU(2)-Higgs model are reproduced via Monte Carlo simulations, in particular the single-Higgs phase structure, which has a region of analytic connection between the symmetric and Higgs phases. The phase structure of the SU(2)-multi-Higgs model is explored for the case of N >= 2 identical Higgs fields. There is no remaining region of analytic connection between the phases, at least when interactions between different Higgs flavours are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for N = 2 by introducing an asymmetry in the hopping parameters of the Higgs fields.

The Higgs boson has an important role in the theoretical formulation of the standard model of fundamental interactions. Symmetry breaking of the vacuum via the Higgs field allows the gauge bosons of the weak interaction and all fermions to acquire mass in a way that preserves gauge-invariance, and thus renormalizablility. The Standard Model can accommodate an arbitrary number of Higgs fields with appropriate charge assignments. To explore the effects of multiple Higgs particles, the SU(2)-multi-Higgs model is studied using lattice simulations, a non-perturbative technique in which the fields are placed on a discrete space-time lattice. The formalism and methods of lattice field theory are discussed in detail. Standard results for the SU(2)-Higgs model are reproduced via Monte Carlo simulations, in particular the single-Higgs phase structure, which has a region of analytic connection between the symmetric and Higgs phases. The phase structure of the SU(2)-multi-Higgs model is explored for the case of N >= 2 identical Higgs fields. There is no remaining region of analytic connection between the phases, at least when interactions between different Higgs flavours are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for N = 2 by introducing an asymmetry in the hopping parameters of the Higgs fields.