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Exact solution Ising-like $2 \times 2 \times \infty$ models with multispin interactions by Khrapov, Pavel; Nikishina, Veronika is a scholarly article available to read on EtoBox.

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The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $\pi/2$, which includes all possible multiplicative interactions of an even number of spins in the unit cube.The exact value of free energy and heat capacity in the thermodynamic limit is found. For percolation invariant with respect to rotation about the central axis of rotation through the angle $\pi/2$, a limit relation for the non-percolation probability is derived. The solution was obtained by the transfer matrix method. In the general case, finding the largest eigenvalue of a $16 \times 16$ transfer matrix reduces to solving a quartic equation using the Ferrari method. In special cases, switching the transfer matrix of models with auxiliary matrices made it possible to reduce the problem to quadratic and linear equations. A separate chapter is devoted to the gonigendrial model in the $2\times2\times\infty$ strip, the exact values of the free energy and heat capacity in the thermodynamic limit are found for the case of free boundary conditions and an analogue of cyclically closed boundary conditions in b

Author

Khrapov, Pavel; Nikishina, Veronika

Published

2022

Language

EN