The critical temperature for the Ising model on planar doubly periodic graphs
Abstract
We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature \beta for a graph G with coupling constants (J_e)_{e\in E(G)} is obtained as the unique solution of a linear equation in the variables (\tanh(\beta J_e))_{e\in E(G)}. This is achieved by studying the high-temperature expansion of the model using Kac-Ward matrices.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2012
- DOI:
- 10.48550/arXiv.1209.0951
- arXiv:
- arXiv:1209.0951
- Bibcode:
- 2012arXiv1209.0951C
- Keywords:
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- Mathematical Physics;
- Mathematics - Probability;
- 82B20
- E-Print:
- 17 pages, 7 figures