A tensor renormalization group analysis of the Blume–Capel model inspired by game theory.

After showing that it can be parametrized as the elementary coordination game of evolutionary game theory, this paper analyzes the Blume–Capel model using the tensor renormalization group method introduced by Michael Levin and Cody P. Nave. The results obtained along the cross sections defined by the coordination game parametrization expand and corroborate earlier findings regarding the location, order, and critical properties of the order–disorder phase transitions in both the zero-field and non-zero-field versions of the Blume–Capel model. • The Blume–Capel model and the elementary coordination game are exactly equivalent. • The crystal field is temperature-dependent along the corresponding cross sections. • These cross sections are studied here using the tensor renormalization group method. • Phase transition results corroborate earlier findings, confirming the equivalence. • Both the zero- and non-zero-field cases are considered. [ABSTRACT FROM AUTHOR]