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By introducing an ansatz, infinite degrees of field freedom of the 1 + 1 dimensional 0(3) nonlinear sigma model are reduced to a single one along the noncontractible loop parameter. The mechanism is examined how the quantum-statistical transition rate of the reduced model by quantum tunneling at low temperatures turns smoothly into that by thermal activation at high temperatures. Such a transition pattern is considered to simulate that of the electroweak theory. At high temperatures, where the transition rate of the reduced model is able to be compared with the field theoretical one, corrections from the field theoretical zero-mode factor and entropy term are found to playa minor role in numerical results.

Sphaleron Transition of Reduced O(3) Nonlinear Sigma Model