Journal of Statistical Physics

, 144:1009

First online:

Mixing Times for the Mean-Field Blume-Capel Model via Aggregate Path Coupling

  • Yevgeniy KovchegovAffiliated withDepartment of Mathematics, Oregon State University
  • , Peter T. OttoAffiliated withDepartment of Mathematics, Willamette University Email author 
  • , Mathew TitusAffiliated withDepartment of Mathematics, Oregon State University

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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 mean-field Blume-Capel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a two-dimensional parameter space there exists a curve at which the model undergoes a second-order, continuous phase transition, a curve where the model undergoes a first-order, 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.


Path coupling Mixing times Glauber dynamics Large deviations Blume-Capel model Aggregate path coupling