Remarks on the Combinatorial Approach to the Ising Problem

DOI10.1063/1.1703907zbMath0151.46602OpenAlexW1974856615MaRDI QIDQ5530968

P. N. Burgoyne

Publication date: 1963

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/872c1194d38c409ced2ff32170420c9adaf3c758

zbMATH Keywords

structure of matter

Related Items (14)

A combinatorial series expansion for the Ising model ⋮ Ising model observables and non-backtracking walks ⋮ Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results ⋮ The signed loop approach to the Ising model: foundations and critical point ⋮ Free fermion approximation for the Ising model with further-neighbor interactions on a triangular lattice ⋮ Phase transition free regions in the Ising model via the Kac-Ward operator ⋮ Feynman identity: a special case revisited ⋮ Feynman identity: A special case. I ⋮ The hypergeometric series for the partition function of the 2D Ising model ⋮ Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function ⋮ On a remarkable class of two-dimensional random walks ⋮ Quantification of spatiotemporal phenomena by means of cellular automata techniques ⋮ Asymptotic expansions for a remarkable class of random walks ⋮ A short proof of the Kac-Ward formula

Cites Work

• Combinatorial Problems Suggested by the Statistical Mechanics of Domains and of Rubber-Like Molecules
• Combinatorial Aspects of the Ising Model for Ferromagnetism. I. A Conjecture of Feynman on Paths and Graphs
• Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
• A Combinatorial Solution of the Two-Dimensional Ising Model
• The Combinatrial Method and the Two-Dimensional Ising Model

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