Information theoretic approach to ground-state phase transitions for two and three-dimensional frustrated spin systems

Abstract

The information theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity) and multi information are used to analyze ground-state spin configurations for disordered and frustrated model systems in 2D and 3D. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.

11 pages, 7 figures, paper summary available at http://www.papercore.org/Melchert2012

References in corpus (6)

• The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing
• Using mutual information to measure order in model glass-formers
• Matching Kasteleyn Cities for Spin Glass Ground States
• Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses
• Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition
• The stability to instability transition in the structure of large scale networks

Cited by in corpus (6)

• Balance and Frustration in Signed Networks
• Analysis of the phase transition in the $2D$ Ising ferromagnet using a Lempel-Ziv string parsing scheme and black-box data-compression utilities
• Thermodynamic description of the Ising antiferromagnet on triangular lattice with selective dilution by modified Pair Approximation method
• Inference of hidden structures in complex physical systems by multi-scale clustering
• Communicating through a geometrically frustrated channel
• Phase transition for parameter learning of Hidden Markov Models