Interpolating between Ising, XY, and nonlinear sigma models
Jan, 1991
19 pages
Published in:
- Nucl.Phys.B 360 (1991) 264-282
- Published: 1991
Report number:
- NBI-HE-91-01,
- FSU-SCRI-91-03
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Abstract: (Elsevier)
The β-functions of O( N )-symmetric non-linear σ-models on the lattice were recently discovered to be non-monotonic for N ⩾ 3. We explain the non-monotonic behaviour as a non-perturbative lattice effect by relating it to the Kosterlitz-Thouless transition of the XY -model. We also relate the latter transition to the phase transition of the Ising model. These relationships are established by interpolating between the O( N )- and the O( N − 1)-symmetric non-linear σ-models by suppression of the N th component of the N -vector field with a mass term. A critical line in the coupling-mass plane connects the critical point of the Ising model ( N = 1) with the critical point of the XY -model ( N = 2). This line extends towards the region of non-monotonic behaviour of the β-function of the O(3)-symmetric model. The nature of the transition lines is also investigated.- Ising model
- XY model
- sigma model: nonlinear
- symmetry: O(N)
- lattice field theory
- critical phenomena
- dimension: 2
- numerical calculations: Monte Carlo
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