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

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

1992-12-01

arxiv.org/abs/cond-mat/9212001v2

Physics

Condensed Matter

10 pages (RevTeX 3.0), 3 PostScript figures (errors fixed) appended, preprint CRPS-92-01

Scientific paper

10.1103/PhysRevB.47.8353

The $O(3)$ nonlinear $\sigma$ 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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