This title appears in the Scientific Report :
2013
Please use the identifier:
http://hdl.handle.net/2128/5928 in citations.
Please use the identifier: http://dx.doi.org/10.1103/PhysRevE.87.022128 in citations.
Information theoretic aspects of the twodimensional Ising model
Information theoretic aspects of the twodimensional Ising model
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2HL(w)−H2L(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This...
Personal Name(s):  Lau, Hon Wai (Corresponding author) 

Grassberger, Peter  
Contributing Institute: 
Jülich Supercomputing Center; JSC 
Published in:  Physical review / E, 87 (2013) 2, S. 022128 
Imprint: 
College Park, Md.
APS
2013

DOI: 
10.1103/PhysRevE.87.022128 
Document Type: 
Journal Article 
Research Program: 
Computational Science and Mathematical Methods 
Link: 
OpenAccess 
Publikationsportal JuSER 
Please use the identifier: http://dx.doi.org/10.1103/PhysRevE.87.022128 in citations.
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2HL(w)−H2L(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference w. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the “excess entropy” for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms et al., and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with w. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of n spins in an infinite lattice diverges at criticality logarithmically with n. We conjecture that such logarithmic divergence happens generically for any onedimensional subset of sites at any twodimensional secondorder phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality. 