Abstract
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972), who later dubbed it the fukinuke, or “noceiling”, model. Defining new spin variables as the product of nearestneighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fukinuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010).
We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fukinuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fukinuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Original language  English 

Pages (fromto)  388404 
Number of pages  17 
Journal  Nuclear Physics B 
Volume  914 
Early online date  11 Nov 2016 
DOIs  
Publication status  Published  Jan 2017 
Keywords
 Statistical thermodynamics
Fingerprint Dive into the research topics of 'Exact solutions to plaquette Ising models with free and periodic boundaries'. Together they form a unique fingerprint.
Profiles

Desmond Alexander Johnston
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)