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The Mass Gap of the Nonlinear Sigma Model through the Finite Temperature Effective Action

D. Senechal
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Abstract

The $O(3)$ nonlinear $σ$ model is studied in the disordered phase, using the techniques of the effective action and finite temperature field theory. The nonlinear constraint is implemented through a Lagrange multiplier. The finite temperature effective potential for this multiplier is calculated at one loop. The existence of a nontrivial minimum for this potential is the signal of a disordered phase in which the lowest excited state is a massive triplet. The mass gap is easily calculated as a function of temperature in dimensions 1, 2 and 3. In dimension 1, this gap is known as the Haldane gap, and its temperature dependence is compared with experimental results.

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D. Senechal. 1992-12-09. The Mass Gap of the Nonlinear Sigma Model through the Finite Temperature Effective Action. https://doi.org/10.1103/physrevb.47.8353

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