Linear Glauber model
Abstract
We study the time-dependent and the stationary properties of the linear Glauber model in a d-dimensional hypercubic lattice. This model is equivalent to the voter model with noise. By using the Green function method, we get exact results for the two-point correlations from which the critical behavior is obtained. For vanishing noise the model becomes critical with exponents β=0, γ=1, and ν=1/2 for d⩾2, with logarithmic corrections at the upper critical dimension dc=2, and β=0, γ=1/2, and ν=1/2 for d=1. We show that the model can be mapped into a particular reaction-diffusion model.
- Publication:
-
Physical Review E
- Pub Date:
- June 2003
- DOI:
- 10.1103/PhysRevE.67.066101
- Bibcode:
- 2003PhRvE..67f6101D
- Keywords:
-
- 02.50.Ey;
- 64.60.Cn;
- 64.60.Ht;
- Stochastic processes;
- Order-disorder transformations;
- statistical mechanics of model systems;
- Dynamic critical phenomena