Particle Systems arising from an anti-ferromagnetic Ising model

Details Particle Systems arising from an anti-ferromagnetic Ising model Particle Systems arising from an anti-ferromagnetic Ising model

2010-08-13

arxiv.org/abs/1008.2310v1

Mathematics

Probability

Scientific paper

We study a low temperature anisotropic anti-ferromagnetic 2D Ising model through the guise of a certain dimer model. This model has a bijection with a one-dimensional particle system equipped with creation and annihilation. In the thermodynamic limit, we determine the explicit phase diagrams as functions of temperature and anisotropy. Two values of the anisotropy are of particular interest - the 'critical' value and the 'independent' value. At independence, the particle system has the same distribution as the two colored noisy voter model. Its limiting measure under a natural scaling window is the Continuum Noisy Voter Model. At criticality, the distribution of particles on a given horizontal line, is a Pfaffian point process whose kernel in the scaling window can be written explicitly in terms of Bessel functions. We also show that `macroscopic' creations form a Poisson point process.

Affiliated with

Also associated with

No associations

Rating

Particle Systems arising from an anti-ferromagnetic Ising model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Particle Systems arising from an anti-ferromagnetic Ising model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Particle Systems arising from an anti-ferromagnetic Ising model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-503234