Discrete approximations to vector spin models

Abstract

We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretising continuous-spin models, and show that, except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.

12 pages

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Cited by in corpus (7)

• A class of nonergodic interacting particle systems with unique invariant measure
• Quasi Long Range Order and Vortex Lattice in the Three State Potts Model
• Phase transitions in $q$-state clock model
• Stability of gas measures under perturbations and discretizations
• Decimations for Two-dimensional Ising and Rotator Models I
• Non-robust phase transitions in the generalized clock model on trees
• Time-periodic behaviour in one- and two-dimensional interacting particle systems