Multicanonical study of $D=2$ $O(3)$ nonlinear $σ$-model

Details Multicanonical study of $D=2$ $O(3)$ nonlinear $σ$-model Multicanonical study of $D=2$ $O(3)$ nonlinear $σ$-model

1994-01-18

arxiv.org/abs/hep-lat/9401018v1

Nucl.Phys.Proc.Suppl. 34 (1994) 667-670

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, PostScript

Scientific paper

10.1016/0920-5632(94)90477-4

We present a new and exploratory approach to determine the $\Delta\beta(\beta)$-shift in the $O(3)$ nonlinear $\sigma$-model. The method is based on a scaling hypothesis for a free energy difference, which is assumed to be valid in a situation where the mass gap correlation length $\xi$ is of the order or larger than the linear extent $L$ of the considered square lattice sizes. The free energy difference arises from the finite volume constraint effective potential of the theory. While the constraint effective potential is calculated in numerical simulations employing a variant of the multicanonical ensemble on medium sized lattices, it is possible to estimate $\Delta\beta(\beta)$ up to a value of $\beta=2.8$ in the standard parameterization of the model.

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