B. Alles, A. Papa
Published 2007-11-09, updated 2008-02-25Version 2
By analytic continuation to real theta of data obtained from numerical simulation at imaginary theta we study the Haldane conjecture and show that the O(3) non-linear sigma model with a theta term in 2 dimensions becomes massless at theta=3.10(5). A modified cluster algorithm has been introduced to simulate the model with imaginary theta. Two different definitions of the topological charge on the lattice have been used; one of them needs renormalization to match the continuum operator. Our work also offers a successful test for numerical methods based on analytic continuation.
Comments: Latex file, 4 pages. To appear in PRD; it contains the justification of analicity, more details about the fits, more references, etc
Journal: Phys.Rev.D77:056008,2008
Analytic continuation over complex landscapes
The $J_1$-$J_2$ spin chain and the $O(3)$ non-linear sigma model at $θ= π$
Order parameter dynamics of the non-linear sigma model in the large $N$ limit
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