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

References in corpus (4)

• Dualities and the phase diagram of the $p$-clock model
• Relative entropy and variational properties of generalized Gibbsian measures
• On Random Field Induced Ordering in the Classical XY Model
• Rotating states in driven clock- and XY-models

Cited by in corpus (7)

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• 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