A Tensor Renormalization Group Analysis of an Evolutionary Game of Competing Ising and Potts Subgames

Király, Balázs (2024) A Tensor Renormalization Group Analysis of an Evolutionary Game of Competing Ising and Potts Subgames. PHYSICS LETTERS A, 502. No.-129392. ISSN 0375-9601 (print); 1873-2429 (online)

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Abstract

The temperature-induced phase transitions of an evolutionary game of competing Ising- and Potts-type coordination subgames are studied using the tensor renormalization group method proposed by Michael Levin and Cody P. Nave. Depending on the relative strength of the subgames, a continuous Ising order to disorder or a continuous Potts order to disorder or consecutive first-order Potts order to Ising order and continuous Ising order to disorder phase transitions are observed. In the game-theoretic interpretation of the model, these results imply that while both types of coordination can spread in the population at low noise levels, one of them will always be dominant in equilibrium. Under a relatively narrow set of circumstances, a small increase in noise can cause the population to suddenly switch from Ising-type coordination to Potts-type coordination. The results are in general qualitative and quantitative agreement with previous Monte Carlo simulation findings.

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