Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs
Copyright policy )Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs
AbstractWe present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the ‘winding’ technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514–527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.
- Queen Mary University of London United Kingdom
- University of Leeds United Kingdom
- Queen Mary University of London
- University of Leeds
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
FOS: Computer and information sciences, Graph operations (line graphs, products, etc.), Randomized algorithms, Probability (math.PR), 68Q25 (Primary) 68Q17, 68Q87, 82B20 (Secondary), Computational Complexity (cs.CC), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Approximation algorithms, Computer Science - Computational Complexity, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Analysis of algorithms, Data Structures and Algorithms (cs.DS), Mathematics - Probability
FOS: Computer and information sciences, Graph operations (line graphs, products, etc.), Randomized algorithms, Probability (math.PR), 68Q25 (Primary) 68Q17, 68Q87, 82B20 (Secondary), Computational Complexity (cs.CC), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Approximation algorithms, Computer Science - Computational Complexity, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Analysis of algorithms, Data Structures and Algorithms (cs.DS), Mathematics - Probability
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