Mixing Times for the MeanField BlumeCapel Model via Aggregate Path Coupling
 Yevgeniy Kovchegov,
 Peter T. Otto,
 Mathew Titus
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We investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the meanfield BlumeCapel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a twodimensional parameter space there exists a curve at which the model undergoes a secondorder, continuous phase transition, a curve where the model undergoes a firstorder, discontinuous phase transition, and a tricritical point which separates the two curves. We determine the interface between the regions of slow and rapid mixing. In order to completely determine the region of rapid mixing, we employ a novel extension of the path coupling method, successfully proving rapid mixing even in the absence of contraction between neighboring states.
 Title
 Mixing Times for the MeanField BlumeCapel Model via Aggregate Path Coupling
 Journal

Journal of Statistical Physics
Volume 144, Issue 5 , pp 10091027
 Cover Date
 201109
 DOI
 10.1007/s1095501102868
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Path coupling
 Mixing times
 Glauber dynamics
 Large deviations
 BlumeCapel model
 Aggregate path coupling
 Industry Sectors
 Authors

 Yevgeniy Kovchegov ^{(1)}
 Peter T. Otto ^{(2)}
 Mathew Titus ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA
 2. Department of Mathematics, Willamette University, Salem, OR, 97302, USA