(1+1)-dimensional O(3) nonlinear σ model in a magnetic field: Magnetization and effective potential

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Abstract
Using the exact solution, we calculate the magnetization and scaling dimensions of correlation functions for the (1+1)-dimensional O(3) nonlinear σ model in a magnetic field. We also describe the renormalization trajectory of this model and obtain explicitly the effective potential for the vector field in the strong-coupling limit. The magnetization curve m(h) exhibits a very early departure from the perturbative behavior; at the same time, the scaling dimensions of correlation functions (in a finite magnetic field, they have power-law asymptotes) are well described by perturbation theory everywhere except for the strong-coupling regime.